Uwe Kähler
Prof. Dr. rer. nat.
Full Professor
University of Aveiro
Coordinator of the group of
Complex and Hypercomplex Analysis
CIDMA
LIST OF PUBLICATIONS
1. (with K. Gürlebeck) On a spatial generalization of the complex P-operator, ZAA, 15(1996) 2, 283 - 297
2. (with K. Gürlebeck) On a boundary value problem of the biharmonic equation, Math. Meth. in the Applied Sciences, Vol. 20 (1997), 867 - 883
3. Clifford Analysis and elliptic boundary value problems over unbounded domains, in Clifford Algebras and their Application in Mathematical Physics, ed. V. Dietrich, K. Habetha and G. Jank, Kluwer Acad. Publ., 1998, 145 - 160
4. (with K. Gürlebeck, J. Ryan e W. Sprößig) Clifford analysis over unbounded domains, Advances in Applied Mathematics, 19 (1997), 216 - 239
5. Application of a hypercomplex P-operator to the solution of Beltrami systems, Proc. of the international symposium “Analytical and numerical methods in Quaternionic and Clifford Analysis”, ed. W. Sprößig and K. Gürlebeck, Research papers of Freiberg, Freiberg, 1997, 69 - 75
6. On the solutions of higher-dimensional Beltrami-equations, Digital Proc. of the IKM 97, Weimar, 1997
7. (with K. Gürlebeck, M.V. Shapiro e L.M. Tovar) On Qp-spaces of quaternion-valued functions , Complex Variables, 39 (1999), 115 - 135
8. (with K. Gürlebeck e M.V. Shapiro) On the P-operator in hyperholomorphic function theory, Advances in Applied Clifford Algebras, 9 (1999), 23 - 40
9. Elliptic Boundary Value Problems in Bounded and Unbounded Domains, in Dirac operators in Analysis, ed. J. Ryan and D. Struppa, Pitman Research Notes in Mathematics 394, Pitman-Longman, 1998, 122 - 144
10. Application of Clifford analysis to the solution of Stokes-equations in unbounded domains, ZAMM, 79 (1999), Suppl. 3, 797 - 798
11. On a direct decomposition of the space Lp (W), ZAA, 18 (1999), 839 - 848
12. Clifford analysis and the Navier-Stokes equations over unbounded domains, Advances in Applied Clifford algebras, 11 (2001) S2, Special issue “Clifford analysis”, 305 - 318
13. (with P. Cerejeiras) Elliptic boundary value problems of fluid dynamics over unbounded domains, Math. Meth. Appl. Sc., 23 (2000), 81 – 101
14. On quaternionic Beltrami equations, in Clifford Algebras and their Application in Mathematical Physics, Vol. II, ed. J.Ryan and W. Sprößig, Birkhäuser, Basel, 2000, 3 - 17.
15. The Navier-Stokes equations over unbounded domains, Proc. of the II. ISAAC-Congress, ed. H. Begehr, R.P. Gilbert, and J. Kajiwara, Kluwer Acad. Publ., 2000, 1431 - 1446
16. (with P. Cerejeiras, K. Gürlebeck e H. Malonek) A quaternionic Beltrami type equation and the existence of local homeomorphic solutions, ZAA, 20 (2001), 17 - 34.
17. (with P. Cerejeiras) On Beltrami equations in Clifford analysis and its quasiconformal solutions, in Clifford Analysis and Its Applications, F. Brackx et al. (eds.), NATO Science Series, II. Mathematics, Physics and Chemistry, vol. 25, Kluwer, 2001, 49 -- 58.
18. (with A.M. Martins) Quaternionic Beltrami-type equations and homeomorphic solutions, Advances in Applied Clifford Algebras, 11 (2001) S1, Special issue “Clifford Analysis and Related Topics”, 177 - 182
19. (with P. Cerejeiras and F. Sommen) Clifford Analysis on Projective Hyperbolic Space , Journal of Natural Geometry, 22 (2002) 1-2, 19 - 34
20. (with P. Cerejeiras and F. Sommen) Clifford Analysis on projective hyperbolic space II, Math. Meth. Appl. Sci. 25 (2002) 16-18, Special edition “Clifford analysis and applications”, 1465 - 1478
21. (with G. Ren) Weighted Hölder continuity of hyperbolic harmonic Bloch functions, ZAA, 21 (2002) 3, 599 - 610
22. (with G. Ren) Weighted Bloch spaces and Gleason's problem, Complex Variables, 48 (2003) 3, 235-245
23. (with G. Ren) Radial Derivative on Bounded Symmetric Domains, Studia Math. 157 (2003) 1, 57 – 70.
24. Multiresolution analysis on Qp-Spaces, Digital Proc. of the IKM 2003, Weimar, 2003
25. (with P.Cerejeiras, S. Dahlke, M. Lindemann, M. J. Soares, G. Teschke, M. Zhariy), A wavelet based numerical method for non-linear partial differential equations , Digital Proc. of the IKM 2003, Weimar, 2003
26. (with G. Ren) Boundary behavior of Gleason's problem in hyperbolic harmonic Bergman space, Science in China A 48 (2005) 2, 145-154.
27. (with G. Ren) Weighted Lipschitz continuity, harmonic Bloch and Besov spaces in the real unit ball, Proc. Edinb. Math. Soc., 48 (2005) 3, 743-755.
28. (with G. Ren) Hardy-Littlewood Inequalities and Qp-Spaces, ZAA, 24 (2005) 2, 375-388.
29. (with P. Cerejeiras and M. Ferreira) Monogenic wavelets over the unit ball, ZAA, 24 (2005) 4, 813-824.
30. (with P. Cerejeiras and F. Sommen) Parabolic Dirac operators and the Navier-Stokes equations over time-varying domains, Math. Meth. Appl. Sci. 28 (2005), 1715-1724.
31. (with P. Cerejeiras, M. Ferreira, and N. Vieira) Monogenic Frames for an integral transform on the unit sphere, Complex Variables, 51 (2006) 1, 51-61.
32. (with G. Ren) Almansi decomposition for polyharmonic, polyheat, and polywave functions, Studia Math. 172 (2006) 1, 91-100.
33. (with N. Faustino, K. Gürlebeck, A. Hommel) Difference potentials for the Navier-Stokes equations in unbounded domains, J. Diff. Eq. & Appl. 12 (2006) 6, 577-596.
34. (with P. Cerejeiras, M. Ferreira) Clifford Analysis and the Continuous Spherical Wavelet Transform, in: Wavelet Analysis and Applications, ed. Q. Tao, etc., Applied and Numerical Harmonic Analysis, Birkhäuser, Basel, 2006, 173-184.
35. Frames for the Continuous Spherical Wavelet Transform, PAMM, 6 (2006), 633-634.
36. (with P. Cerejeiras, M. Ferreira, F. Sommen) Continuous Wavelet Transform and Wavelet Frames on the Sphere Using Clifford Analysis , Comm. Pure Appl. Anal. 6 (2007) 3, 619-641.
37. (with N. Faustino) Fischer Decomposition for Difference Dirac Operators, Adv. Appl. Cliff. Alg., 17 (2007), 37-58.
38. (with N. Faustino, F. Sommen) Discrete Dirac operators in Clifford Analysis , Adv. Appl. Cliff. Alg., 17 (2007) 3, 451-467.
39. (with P. Cerejeiras, V. V. Kravchenko) On a factorization of Schrödinger and Klein-Gordon operators, Math. Meth. Appl. Sci., 31 (2008) 14, 1722-1738.
40. (with G. Bernardes, P. Cerejeiras) Fischer decomposition and Cauchy kernel for Dunkl-Dirac operators , Adv. Appl. Cliff. Alg., 19 (2009) 2, 163-171.
41. (with P. Cerejeiras, M. Fei) Fueter's theorem and its generalizations in Dunkl-Clifford analysis, J. Phys. A: Math. Theor., 42 (2009) 39, 395209-395224.
42. (with G. Ren) Almansi decomposition for poly-ultrahyperbolic functions, Acta Mathematica Sinica, 25 (2009) 9, 1561-1566.
43. (with P. Cerejeiras, Q. Chen) A necessary and sufficient condition for a Bedrosian identity , Math. Meth. Appl. Sci. 33 (2010), 493-500.
44. (with G. Bernardes, S. Bernstein, P. Cerejeiras) Wavelets invariant under finite reflection groups, Math. Meth. Appl. Sci. 33 (2010), 473-484.
45. (with G. Ren) Almansi decomposition for poly-ultrahyperbolic functions, Acta Mathematica Sinica, 25 (2009) 9, 1561-1566.
46. (with P. Cerejeiras, Q. Chen, G. Ren) Chirp transforms and Chirp series, Journal of Mathematical Analysis and Applications , 373 (2011), 356-369.
47. (with P. Cerejeiras, Q. Chen) Bedrosian Identity in Blaschke Product Case, Complex Analysis and Operator Theory 6 (2012) 1, 275-300.
48. (with H. de Ridder, H. de Schepper, F. Sommen) Discrete Function Theories based on Skew-Weyl relations , Proc. of AMS 138 (2010) 9, 3241-3256.
49. (with M. Fei, P. Cerejeiras) Spherical Dunkl-monogenics and a factorization of the Dunkl–Laplacian , J. Phys. A: Math. Theor., 43 (2010) 44, 445202-445216.
50. (with G. Ren, J. Shi, C. Liu) Hardy-Littlewood Inequalities for Fractional Derivatives of Invariant Harmonic Functions, Complex Analysis and Operator Theory 6 (2012) 2, 373-396.
51. (with P. Cerejeiras, M. Ferreira, G. Teschke) Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principles , Appl. Comput. Harmon. Anal., 31 (2011), 325–345.
52. (with P. Cerejeiras, M. Ku), Solutions to a class of polynomially generalized Bers-Vekua equations using Clifford Analysis, Archivum Mathematicum, 48 (2012), 317-331.
53. (with P. Cerejeiras, Y. Fu) The Balian–Low theorem for a new kind of Gabor system , Applicable Analysis, 92 (2013) 4, 799-813.
54. (with M. Ku, D.S. Wang) Riemann boundary value problems on the sphere in Clifford analysis, Advances in Applied Clifford Algebras, 22 (2012), 365-390.
55. (with P. Cerejeiras, M. Ku), Dirichlet-type problems for the iterated Dirac operator on the unit ball in Clifford analysis, em Advances in Hypercomplex Analysis, Springer INdAM Series, ed. Sabadini, I., et. al., 2012, 75-92.
56. (with M. Ku, D.S. Wang) Half Dirichlet problem for the Hölder continuous matrix functions in Hermitian Clifford analysis, Withplex Variables and Elliptic Equations, 58 (2013) 1037-1056.
57. (with M. Ku) On Riemann boundary value problems for polynomial monogenic functions on half space in Clifford analysis, Math. Meth. Appl. Sci., 35 (2012), 2141-2156.
58. (with P. Cerejeiras, Y. Fu) The Balian-Low theorem for the windowed quaternionic Fourier transform, Adv. Appl. Cliff. Alg., 22 (2012), 1025-1040.
59. (with P. Cerejeiras, M. Ku) On the Riemann boundary value problem for null solutions to iterated generalized Cauchy-Riemann operator in Clifford analysis , Results in Mathematics, 63 (2013) 3-4, 1375-1394.
60. (with P. Cerejeiras, Y. Fu, M. Ku) Riemann boundary value problems for iterated Dirac operator on the ball in Clifford analysis , Complex Analysis and Operator Theory, 7 (2013) 3, 673-693.
61. (with P. Cerejeiras, Y. Fu), The Balian-Low theorem for the windowed Clifford Fourier transform, em Quaternion and Clifford Fourier transforms and wavelets, ed. S. Sangwine e E. Hitzer, Birkhäuser, 2013, 299-319.
62. (with P. Cerejeiras, Q. Chen, G. Ren) Non-separable Multivariate Filter Banks from Univariate Wavelets, Mathematische Nachrichten, 286 (2013), 951-969.
63. (with P. Cerejeiras, Y. Fu, L. Li) On the Fock space of metaanalytic functions , Journal of Mathematical Analysis and Applications, 414 (2014), 176-187.
64. (with G. Ren), Pseudohyperbolic metric and uniform discrete sequences in the real unit ball , Acta Mathematica Scientia, 34 (2014) 3, 629-638.
65. (with P. Cerejeiras, M. Rodrigues, N. Vieira), Hodge-type decomposition in variable exponent spaces for the time-dependent operators: the Schroedinger case, Commun. Pure Appl. Anal., 13 (2014) 6, 2253-2287.
66. (with P. Cerejeiras, K. Min, F. Sommen), Discrete Hardy spaces , Journal of Fourier Analysis and Applications, 20, 2014, 715-750.
67. (with S. Bernstein, P. Cerejeiras), Lax pairs for 3D spatial problems based on the Dirac operator , Complex Variables and Elliptic Equations, 59 (2014) 7, 1016-1030.
68. (with N. Vieira), Fractional Clifford Analysis, em Hypercomplex Analysis: New Perspectives and Applications, ed. S. Bernstein et al., Birkhäuser, 2014, 191-202.
69. (with R. Abreu-Blaya, A. Guzman-Adán, J. Bory-Reyes), Symmetries and Associated Pairs in Quaternionic Analysis, em Hypercomplex Analysis: New Perspectives and Applications, ed. S. Bernstein et al., Birkhäuser, 2014, 1-18.
70. (with J. Bory-Reyes, P. Cerejeiras, A. Guzman-Adan), A Short Note on the Local Solvability of the Quaternionic Beltrami Equation , Advances in Applied Clifford Algebras, 2014, doi: 10.1007/s00006-014-0494-9
71. (with P. Cerejeiras, R. Lavicka), Generating Functions for Spherical Harmonics and Spherical Monogenics , Advances in Applied Clifford Algebras, 2014, doi: 10.1007/s00006-014-0495-8
72. (with R. Abreu-Blaya, A. Guzman-Adán, J. Bory-Reyes), On some structural sets and a quaternionic $(\varphi,\psi)$-hyperholomorphic function theory , Mathematische Nachrichten, 288, 2015, 1451-1475.
73. (with P. Cerejeiras, M. Ku), Discrete Hilbert boundary value problems on half lattices , Journal of Difference Equations and Applications, 21 (12), 2015, 1277-1304.
74. (with R. Abreu Blaya, J. Bory Reyes, A. Guzman Adán), On the Π-operator in Clifford analysis , Journal of Mathematical Analysis and Applications, 434, 2016, 1138-1159.
75. (with Fuli He, Min Ku, Pei Dang), Riemann-Hilbert problems for poly-Hardy space on the unit ball, Complex Variables and Elliptic Equations, 6, 2016, 772-790.
76. (with Fuli He, Min Ku, Frank Sommen, Swanhild Bernstein), Riemann-Hilbert problems for monogenic functions in axially symmetric domains , Boundary Value Problems, 22, 2016, 1-11.
77. (with Fuli He, Min Ku, Frank Sommen, Swanhild Bernstein), Riemann–Hilbert problems for null-solutions to iterated generalized Cauchy–Riemann equations in axially symmetric domains , Computers & Mathematics with Applications, 71, 2016, 1990-2000.
78. (with Fuli He, Min Ku), Szegö kernel for Hardy space of matrix functions , Acta Mathematica Scientia, 36, 2016, 203-214.
79. (with R. Abreu Blaya, J. Bory Reyes, A. Guzman Adán), On the Π-operator in Clifford analysis , Journal of Mathematical Analysis and Applications, 434, 2016, 1138-1159.
80. (with P. Cerejeiras, F. Sommen, A. Vajiac), Script Geometry , in Modern Trends in Hypercomplex Analysis, ed. S. Bernstein et al., Birkhaeuser, Basel, 2016, 79-110.
81. (with P. Cerejeiras, M. Ku), Hilbert boundary value problems with Fermionic weight in R^3, Advances in Applied Clifford Algebras, 27, 2017, 87-98.
82. (with N. Gomes, S. Hartmann) Compressed Sensing for Quaternionic Signals , Complex Analysis and Operator Theory, 11, 2017, 417-455.
83. (with M. Ku) Numerical Null-Solutions to Iterated Dirac Operator on Bounded Domains , Complex Analysis and Operator Theory, 11, 2017, 307-328.
84. (with Ricardo Abreu Blaya, Juan Bory Reyes, Alí Guzmán Adán), On the φ-hyperderivative of the ψ-Cauchy-type integral in Clifford analysis , Computational Methods and Function Theory, 17, 2017, 101-119.
85. (with W. Cheng, J. Ryan) Spherical Pi-type operators in Clifford analysis and applications , Complex Analysis and Operator Theory, 11, 2017, 1095-1112.
86. (with K. Guerlebeck, D. Legatiuk) Error Estimates for the Coupling of Analytical and Numerical Solutions , Complex Analysis and Operator Theory, 11, 2017, 1221-1240.
87. (with M. Ku, T. Qian) Schwarz Problems for Poly-Hardy Space on the Unit Ball, Results in Mathematics, 71, 2017, 801-823.
88. (with D. Alpay, P. Cerejeiras) Gleason’s problem associated to the fractional Cauchy-Riemann operator, Fueter series, Drury-Arveson space and related topics , Proceedings of the American Mathematical Society, 145, 2017, 4821-4835.
89. (with D. Bryukhov) The Static Maxwell System in Three Dimensional Axially Symmetric Inhomogeneous Media and Axially Symmetric Generalization of the Cauchy-Riemann System , Advances in Applied Clifford Algebras, 27, 2017, 993-1005.
90. (with M. Ku, Y. Wang, F. He) Riemann–Hilbert Problems for Monogenic Functions on Upper Half Ball of R^4, Advances in Applied Clifford Algebras, 27, 2017, 2493-2508.
91. (with J. Nagler) Detection of C2-singularities using uniform spline approximations , Mathematical Methods in the Applied Sciences, 41, 2018, 303-316
92. (with Lars Abrahamczyk, Zouhour Jaouadi, Dmitrii Legatiuk) Methoden zur Identifikation von Zugvorbeifahrten aus kontinuierlichen Messdaten, Bautechnik, 95, 2018, 485-492.
93. (with T. Fink) A Space-Based Method for the Generation of a Schwartz Function with Infinitely Many Vanishing Moments of Higher Order with Applications in Image Processing, Complex Analysis and Operator Theory, 2018,
94. (with P. Cerejeiras, F. Colombo, I. Sabadini) Perturbation of normal quaternionic operators, Transactions of the American Mathematical Society, https://doi.org/10.1090/tran/7749
95. (with D. Alpay, P. Cerejeiras) Krein reproducing kernel modules in Clifford analysis, Journal d’Análise Mathemátique, 143, 2021, 253-288
96. (with D. Alpay, P. Cerejeiras) General white noise analysis and topological Algebras, Stochastics, 94, 2022, 926-958
97. (with P. Cerejeiras, F. Colombo, I. Sabadini) Quaternionic triangular linear operators, Mathematical Methods in the Applied Sciences 46, 2023, 2093-2116.
98. (with P. Cerejeiras, S. Lucas) Discrete pseudo-differential operators in hypercomplex analysis, Mathematical Methods in the Applied Sciences, 2021, https://doi.org/10.1002/mma.7881.
99. (with D. Alpay, P. Cerejeiras) Generalized Grassmann algebras and applications to stochastic processes, Mathematical Methods in the Applied Sciences, 45, 2022, 383 - 401.
100. (with P. Cerejeiras, T. Fink, B. Forster) Shift-invariant spline subspaces of Sobolev spaces and their order of approximation, Journal of Mathematical Analysis and Applications, 528, 2023, 127444.
