Recent Papers of Luís Castro (since 2005):

  • Finite Interval Convolution Operators with Transmission Property (with R. Duduchava and F.-O. Speck), Integral Equations and Operator Theory 52 (2005), 165–179.
    MSC2000: 47B35 47A05 46E35 45E10
  • On the Invertibility of Prandtl Type Operators in Sobolev Spaces on a Semi-Line, S. Sivasundaram (ed.), ICNPAA 2004: Fifth International Conference on Mathematical Problems in Engineering and Aerospace Sciences, Cambridge: Cambridge Scientific Publishers, 2005, 137–144.
    MSC2000: 47B35 47A05 47A68 46E35 45E10
  • Convolution Operators on Intervals and Their use in Diffraction Theory (with F.-O. Speck), CIM Bulletin 19 (2005), 10–18.
    MSC2000: 47B35 46E10 47A05 46E35 47A20 47A68 78A45 35J05 35J25
  • Inversion of Matrix Convolution Type Operators with Symmetry (with  F.-O. Speck), Port. Math. (N.S.) 62 (2005), 193–216.
    MSC2000: 47B35 47A68
  • Invertibility of Convolution Operators arising in Problems of Wave Diffraction by a Strip with Reactance and Dirichlet Conditions (with B. Zhang), ZAA Zeitschrift für Analysis und ihre Anwendungen 24 (2005), 545–560.
    MSC2000: 47A05, 47A20, 47A68, 47B35, 35J05, 78A45, 42A75, 42A85, 45E10
  • Mixed Boundary Value Problems for the Helmholtz Equation in a Quadrant (with F.-O. Speck and F. S. Teixeira), Integral Equations and Operator Theory 56 (2006), 1–44.
    MSC2000: 35J25, 30E25, 47G30, 45E10, 47A53, 47A20
  • The Reactance Wave Diffraction Problem by a Strip in a Scale of Bessel Potential Spaces (with D. Natroshvili), Opuscula Math. 26 (2006), 289–303.
    MSC2000: 35J05, 35J25, 47A53, 47B35, 47F05, 45E10, 78A45
  • Factorization Theory for Wiener-Hopf plus Hankel Operators with Almost Periodic Symbols (with A. P. Nolasco), Contemp. Math. 414 (2006), 111–128.
    MSC2000: 47B35, 47A68, 47A53, 42A75
  • Wiener-Hopf plus Hankel Operators on the Real Line with Unitary and Sectorial Symbols (with G. Bogveradze), Contemp. Math. 414 (2006), 77–85.
    MSC2000: 47B35, 47A68, 47A53
  • The Potential Method for the Reactance Wave Diffraction Problem in a Scale of Spaces (with D. Natroshvili), Georgian Math. J. 13 (2006), 251–260.
    MSC2000: 35J05, 35J25, 35P25  
  • Asymmetric Factorizations of Matrix Functions on the Real Line (with R. Duduchava and F.-O. Speck), Operator Theory: Advances and Applications 170 (2006), 53–74.
    MSC2000: 47A68, 15A23, 47B35, 15A21
  • Invertibility of Matrix Wiener-Hopf plus Hankel Operators with APW Fourier Symbols (with G. Bogveradze), Int. J. Math. Math. Sci. 38152 (2006), 1–12.
    MSC2000: 47B35, 47A68, 47A53, 42A75   
  • Wave Scattering by an Elastic Obstacle with Interior Cuts (with D. Natroshvili and I. G. Stratis), Math. Nachr. 280 (2007), 996–1013. 
    MSC2000: 31A10, 35J55, 74B05, 74F10
  • On Wave Diffraction by a Half-plane with Different Face Impedances (with D. Kapanadze), Math. Methods Appl. Sci. 30 (2007), 513–527.
    MSC2000: 35J05, 35J25, 35C15, 47H50, 47G30, 47B35 
  • A Duduchava-Saginashvili's Type Theory for Wiener-Hopf plus Hankel Operators (with A. P. Nolasco), J. Math. Anal. Appl. 331 (2007), 329–341. 
    MSC2000: 47B35, 47A68, 47A53, 42A75
  • Mathematical Treatment of a Wave Diffraction Problem with Higher Order Boundary Conditions (with A. M. Simões), in: G. Paltineanu, E. Popescu, I. Toma (ed.), Trends and Challenges in Applied Mathematics, Bucharest: Matrix Rom Publishers, 2007, 44–49.
    MSC2000: 35J05, 35J25, 47B35, 47A53
  • A Boundary-Transmission Problem with First and Second Kind Conditions for the Helmholtz Equation in Besov and Bessel Potential Spaces (with D. Kapanadze), Bull. Greek Math. Soc. 54 (2007), 79–96.
    MSC2000: 35J05, 35J25, 35C15, 47H50
  • A Stronger Version of the Sarason's Type Theorem for Wiener-Hopf-Hankel Operators with SAP Fourier Symbols (with A. P. Nolasco), Bull. Greek Math. Soc. 54 (2007), 59–77. 
    MSC2000: 47B35, 47A68, 47A53, 42A75
  • On the Fredholm Property and Index of Wiener-Hopf plus/minus Hankel Operators with Piecewise Almost Periodic Symbols (with G. Bogveradze), Appl. Math. Inform. Mech. 12 (2007), 25–40.
    MSC2000: 47B35, 47A53, 47A68, 42A75
  • The Impedance Boundary-Value Problem of Diffraction by a Strip (with D. Kapanadze), J. Math. Anal. Appl. 337 (2008), 1031–1040. 
    MSC2000: 35J05, 35J25, 35C15, 47H50
  • Mathieu Function and Kontorovich-Lebedev Transforms in the L-shaped Wave Scattering Problem (with A. H. Kamel), Afr. Diaspora J. Math 5 (2008), 145-161.
    MSC2000: 30E25, 33E10, 35J05, 44A15, 45H05
  • Invertibility Properties of Matrix Wiener-Hopf plus Hankel Integral Operators (with G. Bogveradze), Mathematical Modelling and Analysis 13(1) (2008), 7–16. 
    MSC2000: 47B35, 47A53, 47A68, 42A75
  • Diffraction by a Strip and by a Half-plane with Variable Face Impedances (with D. Kapanadze), Operator Theory: Advances and Applications 181 (2008), 159–172.
    MSC2000: 35J05, 35J25, 35C15, 47H50
  • Diffraction by a Union of Strips with Impedance Conditions in Besov and Bessel Potential Spaces (with D. Kapanadze), Mathematical Modelling and Analysis 13(2) (2008), 183–194. 
    MSC2000: 35J05, 35J25, 35C15, 47H50
  • On the Fredholm Index of Matrix Wiener-Hopf plus/minus Hankel Operators with Semi-Almost Periodic Symbols (with G. Bogveradze), Operator Theory: Advances and Applications 181 (2008), 143–158.
    MSC2000: 47A53, 47B35, 47A68, 42A75
  • Wave Diffraction by a 45 Degrees Wedge Sector with Dirichlet and Neumann Boundary Conditions (with D. Kapanadze), Mathematical and Computer Modelling 48 (2008), 114–121.
    MSC2000: 35J05, 35J25, 35C15, 47H50, 47G30  
  • Solvability of Singular Integro-Differential Equations with Multiple Complex Shifts (with R. Duduchava and F.-O. Speck), Complex Analysis and Operator Theory 2 (2008), 327–343.
    MSC2000: 45E10, 47B35, 47A53, 47A68 
  • Pseudo-differential Operators in a Wave Diffraction Problem with Impedance Conditions (with D. Kapanadze), Fractional Calculus & Applied Analysis 11 (2008), 15–26.
    MSC2000: 35J05, 35J25, 35C15, 47H50, 47G30  
  • Analytical Investigation of the Effective Properties of 2D Composite Materials (with E. Pesetskaya), in: A. J. M. Ferreira (ed.) et al, Proceedings of the International Conference on Mathematics and Continuum Mechanics, Centro Internacional de Matemática, 2008, 13–18.
    MSC2000: 30D05, 30E25, 35B27, 74Q05  
  • Similarity Transformation Methods for Singular Integral Operators with Reflection on Weighted Lebesgue Spaces (with E. M. Rojas), Int. J. Mod. Math. 3(3) (2008), 295–313.  
  • Wave Diffraction by a Strip with First and Second Kind Boundary Conditions: The Real Wave Number Case (with D. Kapanadze), Math. Nachr. 281(10) (2008), 1400–1411.
    MSC2000: 35J05, 35J25, 35C15, 47H50  
  • Reduction of Singular Integral Operators with Flip and Their Fredholm Property (with E. Rojas), Lobachevskii J. Math. 29(3) (2008), 119–129.
    MSC2000: 47G10, 47B35, 47A53, 45E05, 45F15, 47A20  
  • Toeplitz Plus Hankel Operators with Infinite Index (with G. Bogveradze), Integral Equations and Operator Theory 62(1) (2008), 43–63.
    MSC2000: 47B35, 47A53, 47A68, 42A75  
  • Dirichlet-Neumann-impedance Boundary-value Problems Arising in Rectangular Wedge Diffraction Problems (with D. Kapanadze), Proceedings of the American Mathematical Society 136 (2008), 2113–2123.
    MSC2000: 35J05, 35J25, 35C15, 47H50  
  • Invertibility of Matrix Wiener-Hopf plus Hankel Operators with Symbols Producing a Positive Numerical Range (with A. S. Silva), Zeitschrift für Analysis und ihre Anwendungen 28(1) (2009), 119–127.
    MSC2000: 47B35, 47A05, 47A12, 47A20, 42A75.  
  • Invertibility Characterization of Wiener-Hopf plus Hankel Operators Via Odd Asymmetric Factorizations (with G. Bogveradze), Banach J. Math. Anal. 3(1) (2009), 1–18.
    MSC2000: 47B35, 47A68, 47A53  
  • A Criterion for Lateral Invertibility of Matrix Wiener-Hopf plus Hankel Operators with Good Hausdorff Sets (with A. P. Nolasco), in: More Progresses in Analysis (H. G. W. Begehr and F. Nicolosi, eds), Hackensack, NJ: World Scientific Publishing, 2009, 349–358.
    MSC2000: 47B35, 47A68, 47A05, 42A75  
  • Explicit Operator Relations for Singular Integral Operators with a Flip on a Weighted Lebesgue Space (with E. M. Rojas), in: Mathematical Problems in Engineering and Aerospace Sciences (S. Sivasundaram, ed.), Cambridge: Cambridge Scientific Publishers, 2009, 543-550.
    MSC2000: 47G10, 47A53, 45E05, 45F15, 47A20  
  • Fredholm Analysis for a Wave Diffraction Problem with Higher Order Boundary Conditions on a Strip (with A. M. Simões), in: Mathematical Problems in Engineering and Aerospace Sciences (S. Sivasundaram, ed.), Cambridge: Cambridge Scientific Publishers, 2009, 535-542.
    MSC2000: 47A53, 35J25, 78A45, 47A20, 47B35, 45E10  
  • Hyers-Ulam-Rassias Stability for a Class of Nonlinear Volterra Integral Equations (with A. Ramos), Banach J. Math. Anal. 3(1) (2009), 36–43.
    MSC2000: 45D05, 26D10, 34K20, 47H10  
  • Effective Conductivity of a Composite Material with Non-ideal Contact Conditions (with E. Pesetskaya and S. Rogosin), Complex Variables and Elliptic Equations 54 (2009), 1085–1100. 
    MSC2000: 30E25, 35B27, 74Q05  
  • Fredholm Analysis for a Wave Diffraction Problem with Higher Order Boundary Conditions on a Union of Strips (with A. M. Simões), American Institute of Physics, AIP - Conf. Proc. 1186 (2009), 49–56.
    MSC2000: 47A53, 35J25, 78A45, 47A20, 47B35, 45E10.  
  • A Semi-Fredholm Theory for Wiener-Hopf-Hankel Operators with Piecewise Almost Periodic Fourier Symbols (with A.P. Nolasco), Journal of Operator Theory 62(1) 2009, 3–31. 
    MSC2000: 47B35, 47A68, 47A53, 42A75  
  • A Transmission Problem with Imperfect Contact for an Unbounded Multiply Connected Domain (with E. Pesetskaya), Mathematical Methods in the Applied Sciences 33 (2010), 517–526.
    MSC2000: 30E25, 30D05, 31A05, 35B27, 39B32, 74E30, 74G10, 74M15, 74Q05 
  • Fredholm Characterization of Wiener-Hopf-Hankel Integral Operators with Piecewise Almost Periodic Symbols (with G. Bogveradze), in: Integral Methods in Science and Engineering (C. Constanda et al., eds.), Boston: Birkhäuser, 2010, 65–74.
    MSC2000: 47B35, 47A53, 47A68, 42A75.  
  • Hyers-Ulam and Hyers-Ulam-Rassias Stability of Volterra Integral Equations with a Delay (with A. Ramos), in: Integral Methods in Science and Engineering (C. Constanda et al., eds.), Boston: Birkhäuser, 2010, 85–94.
    MSC2000: 45M10, 45D05, 34K20.  
  • Source Inversion of Heat Conduction from a Finite Number of Observation Data (with Q. Chen and S. Saitoh), Applicable Analysis 89(6) (2010), 801–813.
    MSC2000: 30E25, 35B27, 74Q05.  
  • Fredholm Index Formula for a Class of Matrix Wiener-Hopf Plus and Minus Hankel Operators with Symmetry (with A. Silva), in: Integral Methods in Science and Engineering (C. Constanda et al., eds.), Boston: Birkhäuser, 2010, 95–104.
    MSC2000: 47B35, 47A53, 42A75.  
  • Invertibility of Singular Integral Operators with Flip through Explicit Operator Relations (with E. M. Rojas), in: Integral Methods in Science and Engineering (C. Constanda et al., eds.), Boston: Birkhäuser, 2010, 105–114.
    MSC2000: 47G10, 47A53, 45E05, 45F15, 47A20.  
  • Exterior Wedge Diffraction Problems with Dirichlet, Neumann and Impedance Boundary Conditions (with D. Kapanadze), Acta Appl. Math. 110 (2010), 289–311.
    MSC2000: 35J25, 35J05, 45E10, 47A20, 47G30, 47B35, 47H50  
  • Inversion from different kinds of information and real inversion formulas of the Laplace transform from a finite number of data (with E.M. Rojas and S. Saitoh), Math. Eng. Sci. Aerosp. MESA 1(2) (2010), 181–190.
    MSC2000: 44A10, 46E22, 47A52, 44A15, 30C40.  
  • Explicit solutions of Cauchy singular integral equations with weighted Carleman shift (with E. M. Rojas), Journal of Mathematical Analysis and Applications 371 (2010), 128–133.
    MSC2000: 47G10, 47A68, 45E05, 45P05, 30E25, 47B37  
  • Discretization by the theory of reproducing kernels (with S. Saitoh, Y. Sawano and A. M. Simões), RIMS Kôkyûroku 1719 (2010), 142154.
  • On the Solvability of a Problem of Wave Diffraction by a Union of a Strip and a Half-Plane (with A. M. Simões), American Institute of Physics, AIP - Conf. Proc. 1301 (2010), 85–96.
    PACS: 02.30.Tb; 43.20.Bi; 41.20.Jb; 02.30.Jr; 02.30.Sa; 02.30.Rz; 02.30.Uu.  
  • Wiener-Hopf plus Hankel Operators with Almost Periodic Symbols on Weighted Lebesgue Spaces (with A. S. Silva), American Institute of Physics, AIP - Conf. Proc. 1301 (2010), 77–84.
    PACS: 02.30.Tb, 02.30.Rz, 02.30.Sa  
  • Bounds for the Kernel Dimension of Singular Integral Operators with Carleman Shift (with E. M. Rojas), American Institute of Physics, AIP - Conf. Proc. 1301 (2010), 68–76.
    PACS: 02.30.Tb, 02.30.Rz, 02.30.Sa  
  • A collocation method for singular integral operators with reflection (with E. M. Rojas), RIMS Kôkyûroku 1719 (2010), 155167.
  • Fredholm property of matrix Wiener-Hopf plus and minus Hankel operators with piecewise almost periodic symbols (with A. S. Silva), Bull. Greek Math. Soc. 57 (2010), 99–113.
  • Moore-Penrose invertibility of singular integral operators with Carleman shift, Bull. Greek Math. Soc. 57 (2010), 83–97.
  • Fredholm Property of Matrix Wiener-Hopf plus and minus Hankel Operators with Semi-Almost Periodic Symbols (with A. S. Silva), Cubo 12(2) (2010), 217–234.
    MSC2000: 47B35, 47A05, 47A12, 47A20, 42A75.  
  • Wiener-Hopf and Wiener-Hopf-Hankel operators with piecewise almost periodic symbols on weighted Lebesgue spaces (with A. S. Silva), Memoirs on Differential Equations and Mathematical Physics 53 (2011), 39–62. 
    MSC2000: 47B35, 42A75, 47A53, 47A68, 47G10.  
  • On the invertibility of classes of integral operators via generalized factorizations (with A. S. Silva), American Institute of Physics, AIP - Conf. Proc. 1404 (2011), 242–249.  PACS: 02.30.Tb; 02.30.Rz; 02.30.Sa
  • Semi-Fredholm Theory for Wiener-Hopf-Hankel Operators on Muckenhoupt Weighted Lebesgue Spaces (with A. S. Silva), MESA – Mathematics in Engineering, Science and Aerospace 2, No. 4 (2011), 341–353. MSC2000: 47B35, 47A53, 42A75.
  • Hyers-Ulam Stability for a Class of Fredholm Integral Equations (with A. Ramos), Proceedings of the 8th International Conference of Mathematical Problems in Engineering, Aerospace and Science, Cambridge Scientific Publishers (ISBN: 978-1-908106-18-6), UK, 2011, 171–176. MSC2000: 45M10, 45D05, 34K20.
  • Wiener-Hopf-Hankel Operators with Semi-almost Periodic Symbols on Weighted Lebesgue Spaces (with A. S. Silva), Proceedings of the 8th International Conference of Mathematical Problems in Engineering, Aerospace and Science, Cambridge Scientific Publishers (ISBN: 978-1-908106-18-6), UK, 2011, 193–202. MSC2000: 45M10, 45D05, 34K20.
  • Splitting Property for Singular Integral Operators with a Weighted Shift (with E. M. Rojas), Proceedings of the 8th International Conference of Mathematical Problems in Engineering, Aerospace and Science, Cambridge Scientific Publishers (ISBN: 978-1-908106-18-6), UK, 2011, 177–184.
  • Continuous coefficient representations for singular integral operators with shift (with E. M. Rojas), Proceedings of the 8th International Conference of Mathematical Problems in Engineering, Aerospace and Science, Cambridge Scientific Publishers (ISBN: 978-1-908106-18-6), UK, 2011, 185–192.
  • Electromagnetic scattering by cylindrical orthotropic waveguide irises (with D. Kapanadze and R. Duduchava), Georgian Mathematical Journal 18 (2011), 99–120.
    MSC2000: 30E25, 35B27, 74Q05.  
  • On the invertibility of singular integral equations with reflection on the unit circle (with E. Rojas), Integral Equations and Operator Theory 70 (2011), 63–99.
    MSC2000: 45E05, 30E20, 30E25, 45E10, 47A68, 47G10.    
  • General inhomogeneous discrete linear partial differential equations with constant coefficients on the whole spaces (with S. Saitoh, Y. Sawano and A. Simões), Complex Analysis and Operator Theory 6 (2012), 307–324.
    MSC2000: 47B35, 47A05, 47A12, 47A20, 42A75.  
  • Defect numbers of singular integral operators with Carleman shift and almost periodic coefficients (with A. S. Silva), J. Math. Anal. Appl. 387 (2012), 66–76.
    MSC2000:
    47B35, 45E05, 47A68, 47B37, 47G10, 47A53, 42A75.  
  • Applications of reproducing kernels to fractional functions and convolution integral equations (with S. Saitoh), Hokkaido University Technical Report Series in Mathematics 152 (2012), 57–63. MSC2000: 45E10, 46E22, 47A30, 47B32, 47B38, 47G10.
  • Integral equation methods in problems of wave diffraction by a strip with higher order reactance conditions (with A.M. Simões), American Institute of Physics, AIP - Conf. Proc. 1493, 904–910, NY, 2012.
  • Natural outputs and global inputs of linear systems with a finite number of input data (with S. Saitoh), Appl. Anal. 91(2), (2012) 225–236. 
    MSC2000: 44A15; 46E22; 35K05; 30C40; 35L05.  
  • Fundamental error estimate inequalities for the Tikhonov regularization using reproducing kernels (with H. Fujiwara, S. Saitoh, Y. Sawano, A. Yamada, M. Yamada), Inequalities and Applications, International Series of Numerical Mathematics 161, Birkhauser Verlag, 87–101, 2012.
  • Discrete Linear Differential Equations (with S. Saitoh, Y. Sawano, A. S. Silva), Analysis, 32 (2012), 181198. MSC2010: 34A25, 34B05, 30C40, 46E22, 47B32, 47A52.
  • A new discretization method by means of reproducing kernels (with H. Fujiwara, M.M. Rodrigues, S. Saitoh), L.H. Son, W. Tutschke, edts, Interactions between Real and Complex Analysis, 185—223, Science and Technics Publishing House, Ministry for Science and Technology of Vietnam, Ha Noi, 2012.
  • Applications of reproducing kernels to fractional functions and convolution inequalities (with S. Saitoh), Progress in Analysis, Volume 1 (eds.: V. Burenkov et al.), Moscow, Peoples' Friendship University of Russia, 2012, 230—237.
  • Numerical Solutions of Linear Singular Integral Equations by means of Tikhonov Regularization and Reproducing Kernels (with H. Itou and S. Saitoh), Houston Journal of Mathematics, 38(4) (2012), 1261—1276. 
    MSC2000: 45E05, 45L05, 30C40, 65R20.  
  • Wiener-Hopf-Hankel operators with piecewise continuous Fourier Symbols on variable exponent Lebesgue spaces (with A.S. Silva), L.H. Son, W. Tutschke, edts, Interactions between Real and Complex Analysis, 243—255, Science and Technics Publishing House, Ministry for Science and Technology of Vietnam, Ha Noi, 2012.
  • Convolutions, integral transforms and integral equations by means of the theory of reproducing kernels (with S. Saitoh and N. M. Tuan), Opuscula Mathematica, 32(4) (2012), 633—646. MSC2010: 30C40, 42A85, 45E10, 44A20, 46H05.  
  • New convolutions and norm inequalities (with S. Saitoh), Mathematical Inequalities & Applications 15 (2012), 707716.  
  • Wave diffraction by a half-plane with an obstacle perpendicular to the boundary (with D. Kapanadze), Journal of Differential Equations 254 (2013), 493—510. MSC2010: 35J25, 35J05, 45E10, 47A20, 47G30, 47B35, 47H50.
  • Fractional Functions and their Representations (with S. Saitoh), Complex Analysis and Operator Theory 7(4) (2013), 1049—1063. DOI: 10.1007/s11785-011-0154-1. MSC2010: 46E22, 30C40, 42A38, 47B32.       
  • Explicit integral representations of implicit functions (with K. Murata, S. Saitoh and M. Yamada), Carpathian Journal of Mathematics 29(2) (2013), 141—148.  MSC2010: 26B10, 30C40, 47J07, 93C10. 
  • Mixed boundary value problems of diffraction by a half-plane with a screen/crack perpendicular to the boundary (with D. Kapanadze), Proc. A. Razmadze Math. Inst. 162 (2013), 121—126. MSC2010: 35J05, 35L05, 35L20, 78A45.
  • Hyers-Ulam-Rassias stability of Volterra integral equations within weighted spaces (with R.C. Guerra), Libertas Mathematica (new series) 33 (2013), 21—35. MSC2010: 45M10, 45D05, 34K20, 39B82, 47H99.
  • The Weierstrass—Whittaker integral transform (with M.M. Rodrigues), Memoirs on Differential Equations and Mathematical Physics 60 (2013), 57—72.
  • The impedance problem of wave diffraction by a strip with higher order boundary conditions (with A.M. Simões), American Institute of Physics, AIP - Conf. Proc., M. D. Todorov et al, 184—193, NY, 2013.
  • Optimal and approximate solutions of singular integral equations by means of reproducing kernels (with S. Saitoh), Complex Analysis and Operator Theory 7 (2013), 1839—1851.   DOI 10.1007/s11785-012-0254-6.
  • Invertibility Criteria for Wiener-Hopf plus Hankel Operators with Different Almost Periodic Fourier Symbol Matrices (with A. S. Silva), Annali di Matematica Pura ed Applicata 192 (2013), 11411152.   DOI 10.1007/s10231-012-0262-1.
  • Mixed boundary value problems of diffraction by a half-plane with an obstacle perpendicular to the boundary (with D. Kapanadze), Mathematical Methods in Applied Sciences 37 (2014), 1412-1427. MSC2010: 35J05, 35L05, 35L20, 78A45.
  • Quadratic Fourier transforms (with M.R. Haqueb, M.M. Murshed, S. Saitoh, N.M. Tuan), Annals of Functional Analysis, 5(1) (2014), 10—24. MSC2010: 42A38, 30C40, 32A36, 46E22.
  • Aveiro Discretization Method in Mathematics: A New Discretization Principle (with H. Fujiwara, M. M. Rodrigues, S. Saitoh and V.K. Tuan), in: Mathematics without Boundaries: Surveys in Pure Mathematics, Panos Pardalos  and  Themistocles M. Rassias (edts.),  Springer-Verlag, New York, 3792, 2014.  MSC2010: 45E05;  30C40, 42A85, 45E10, 45L05, 44A20, 46H05, 47A30, 47B32, 47B38, 47G10, 65R20.
  • A Bessel differential heat initial value problem in a reproducing kernel Hilbert space framework (with M.M. Rodrigues and S. Saitoh), American Institute of Physics, AIP - Conf. Proc. 1637 (2014), 165170.
  • How to catch smoothing properties and analyticity of functions by computers? (with H. Fujiwara, T. Qian, S. Saitoh), in: Mathematics without Boundaries: Surveys in Interdisciplinary Research, Panos Pardalos  and  Themistocles M. Rassias (edts.),  Springer-Verlag, New York, 101116, 2014. MSC2010: 30C40, 42A85, 45E10, 44A20, 46H05.
  • Diffraction from polygonal-conical screens, an operator approach (with R. Duduchava and F.-O. Speck), Oper. Theory Adv. Appl. 242 (2014), 113—137.
  • Initial value problems in linear integral operator equations (with M.M. Rodrigues, S. Saitoh), in: Topics in Mathematical Analysis and Applications, Panos Pardalos  and  Themistocles M. Rassias and Laszlo Toth (edts.), Springer-Verlag, New York, 175—188, 2014.  MSC2010: 45C05, 32A30, 42A38, 45A05, 45D05, 45E05, 45P05, 46E22, 47A05.
  • A reproducing kernel Hilbert space constructive approximation for integral equations with Toeplitz and Hankel kernels (with A.S. Silva and S. Saitoh), Libertas Mathematica (New Series) 34(1) (2014), 1—22. MSC2010: 45E10, 15A09, 30C40, 42A85, 44A35, 45N05, 46E22, 47A05, 47B35.
  • Diffraction by a half-plane with different face impedances on an obstacle perpendicular to the boundary (with D. Kapanadze), Communications in Mathematical Analysis 17(2) (2014), 4565.  MSC2010: 35J05; 35J25; 35J67; 35S05; 45E10; 46E35; 47A53; 47G30; 47G40; 78A45.
  • Interplay of Wiener-Hopf and Hankel operators with almost periodic Fourier symbols on standard and variable exponent Lebesgue spaces (with A.S. Silva), Annals of Functional Analysis 6(2) (2015), 49—59. MSC2010: 47B35, 47A53, 47A05, 47A20, 42A75.  
  • Wave diffraction by wedges having arbitrary aperture angle (with D. Kapanadze), Journal of Mathematical Analysis and Applications 421 (2015), 1295—1314. MSC2010: 35J05; 35J25; 35J67; 35S05; 45E10; 46E35; 47A53; 47G30; 47G40; 78A45.
  • A fundamental theorem on initial value problems by using the theory of reproducing kernels (with M.M. Rodrigues and S. Saitoh), Complex Analysis and Operator Theory 9(1) (2015), 8798. MSC2010: 58J47, 32A25, 45Q05, 46E22, 47A70, 47B32.
  • Solvability of singular integral equations with rotations and degenerate kernels in the vanishing coefficient case (with E.M. Rojas, S. Saitoh, N.M. Tuan and P.D. Tuan), Analysis and Applications 13(1) (2015), 1—21. DOI: 10.1142/S0219530514500468
  • A heat conduction problem of 2D unbounded composites with imperfect contact conditions (with D. Kapanadze and E. Pesetskaya), ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 95 (9) (2015), 952—965. MSC2010: 30E25, 35B27, 74Q05.
  • Crack impedance-Dirichlet boundary value problems of diffraction in a half-plane (with D. Kapanadze), MESA 6(3) (2015), 551—566. MSC2010: 35J05; 35B30; 35C15; 35J25; 35P25; 47A20; 47A53; 47A68; 47B35; 47G30; 78A45.
  • Reproducing kernels and discretization (with H. Fujiwara, M.M. Rodrigues, S. Saitoh, V.K. Tuan), in: V. Mityushev, M.V. Ruzhansky (eds.), Current Trends in Analysis and Its Applications, 553—559, Springer/Birkhäuser, Basel, 2015. MSC2010: 30C40, 44A05, 44A15, 35K05.
  • On integral operators generated by the Fourier transform and a reflection (with R.C. Guerra and N.M. Tuan), Memoirs on Differential Equations and Mathematical Physics 66 (2015), 7—31. MSC2010: 42B10; 43A3; 44A20; 47A05.
  • Effective conductivity of a composite material with stiff imperfect contact conditions (with D. Kapanadze and E. Pesetskaya), Mathematical Methods in Applied Sciences 38(18) (2015), 4638—4649. MSC2010: 30D05, 30E25, 35B27, 74Q05.
  • L.P. Castro, E. Pesetskaya: Properties of a composite material with mixed imperfect contact conditions (http://hdl.handle.net/10773/15634 and https://sweet.ua.pt/castro/p/2016/CaPe2016MMA.pdf), Mathematical Modelling and Analysis, 21(3), 2016, 283-303.
  • L.P. Castro, S. Saitoh, A. Yamada: Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces (http://hdl.handle.net/10773/16216 and http://link.springer.com/article/10.1007/s11785-016-0545-4), Complex Analysis and Operator Theory, 10(8), 2016, 1705-1723.
  • L.P. Castro, A.S. Silva: On the kernels of Wiener-Hopf-Hankel operators on variable exponent Lebesgue spaces (http://hdl.handle.net/10773/15190 and https://sweet.ua.pt/castro/p/2016/2016CaSi.pdf), Math. Eng. Sci. Aerosp. MESA, 7(2), 2016, 375-386.
  • L.P. Castro, A.S. Silva: Invertibility characterization of Wiener-Hopf plus Hankel operators on variable exponent Lebesgue spaces via even asymmetric factorization (http://hdl.handle.net/10773/16229 and http://dx.doi.org/10.1515/gmj-2016-0048), Georgian Mathematical Journal, 23(4), 2016, 477-488.
  • P.K. Anh, L.P. Castro, P.T. Thao, N.M. Tuan: Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weights (http://hdl.handle.net/10773/16734 and http://dx.doi.org/10.1063/1.4972598), American Institute of Physics, AIP Proceedings, 1798(1), 020006, 10pp., NY, 2017.
  • L.P. Castro, A.M. Simões: Hyers-Ulam and Hyers-Ulam-Rassias stability of a class of integral equations on finite intervals (http://hdl.handle.net/10773/18069), Proceedings of the 17th International Conference on Computational and Mathematical Methods in Science and Engineering, J. Vigo-Aguiar et al, 507-515, Spain, 2017.
  • L.P. Castro, R.C. Guerra, N.M. Tuan: Heisenberg uncertainty principles for an oscillatory integral operator (http://hdl.handle.net/10773/16729 and http://dx.doi.org/10.1063/1.4972629), American Institute of Physics, AIP Proceedings, 1798(1), 020037, 10pp., NY, 2017.
  • L.P. Castro, A.S. Silva: Odd asymmetric factorization of Wiener-Hopf plus Hankel operators on variable exponent Lebesgue spaces (http://hdl.handle.net/10773/16735 and http://dx.doi.org/10.1063/1.4972630), American Institute of Physics, AIP Proceedings, 1798(1), 020038, 10pp., NY, 2017.
  • L.P. Castro, R.C. Guerra, N.M. Tuan: On a class of integral equations involving kernels of cosine and sine type (http://hdl.handle.net/10773/18542, http://link.springer.com/chapter/10.1007%2F978-3-319-59384-5_5 and https://sweet.ua.pt/castro/p/2017/2017PostPrint_CaGuTu.pdf), C. Constanda et al. (Eds.), Integral Methods in Science and Engineering, 47-57, Birkhäuser, Springer, Basel, 2017.
  • L.P. Castro, A.M. Simões: Hyers-Ulam and Hyers-Ulam-Rassias stability of a class of Hammerstein integral equations (http://hdl.handle.net/10773/16736 and http://dx.doi.org/10.1063/1.4972628), American Institute of Physics, AIP Proceedings, 1798(1), 020036, 10pp., NY, 2017.
  • L.P. Castro, F.-O. Speck: Convolution type operators with symmetry in Bessel potential spaces (http://link.springer.com/chapter/10.1007/978-3-319-47079-5_2 and https://sweet.ua.pt/castro/p/2017/2017_CS_OTAApostprint.pdf), V. Mazya, D. Natroshvili, E. Shargorodsky, W. L. Wendland (Eds.), Recent Trends in Operator Theory and Partial Differential Equations - The Roland Duduchava Anniversary Volume, 21-49, Operator Theory: Advances and Applications 158, Birkhäuser, Basel, 2017.
  • P.K. Anh, L.P. Castro, P.T. Thao, N.M. Tuan: Two new convolutions for the fractional Fourier transform (http://hdl.handle.net/10773/16666, http://link.springer.com/article/10.1007/s11277-016-3567-3 and https://sweet.ua.pt/castro/p/2017/2017PostPrintACTT.pdf), Wireless Personal Communications, 92(2), 2017, 623-637.
  • L.P. Castro, A.M. Simões: Different types of Hyers-Ulam-Rassias stabilities for a class of integro-differential equations (http://hdl.handle.net/10773/21063 and http://www.pmf.ni.ac.rs/pmf/publikacije/filomat/filomat_pocetna.php), Filomat, 31(17), 2017, 5379-5390.
  • L.P. Castro, L.T. Minh, N.M. Tuan: New convolutions for quadratic-phase Fourier integral operators and their applications (http://hdl.handle.net/10773/21367, http://rdcu.be/DWRU and https://doi.org/10.1007/s00009-017-1063-y), Mediterranean Journal of Mathematics, 15 (13), 2018, 1-17.
  • L.P. Castro, E. Pesetskaya: A composite material with inextensible-membrane-type interface (https://doi.org/10.1177/1081286517746717) Online First Published: January 15, 2018, Mathematics and Mechanics of Solids, 12 pp.
  • L.P. Castro, A.M. Simões: Hyers-Ulam-Rassias stability of nonlinear integral equations through the Bielecki metric, Mathematical Methods in the Applied Sciences, to appear, 17 pp.

 

 

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Last Update: 2018

 

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