International Intensive Courses

dedicated to Dirac operators, Hypercomplex and Harmonic Analysis

Please pay attention to the following rules for the online courses:


  1. It is highly appreciated if you use your real and complete name when entering the system. 

  1. Switch your microphone off when the lecture begins. You can switch it back when asking questions or replying. 


The videos of the lectures will be made available to all registered participants at the end of the course.

Any un-authorized recording and distribution is illegal and it will be reported to the competent authorities.

Time zone converter

Most common time zones (recall, some countries changed already to Standard Time, or Winter Time):

  1. CET zone (Central European Time)

  2. PST zone (Pacific Standard Time)

  3. CST (China Standard Time)

The online series of International Intensive Courses dedicated to Dirac operators, Hypercomplex and Harmonic Analysis are jointly organized by Chapman University, Politecnico di Milano, and University of Aveiro. These sequence of events will take place online and are directed to postgraduate students, young researchers, and all who wishes to expand their knowledge on current topics in these and related areas.

Courses will occur with a trimestral frequency. Interested participants are kindly request to register via e-mail

1st Course - November 23 to December 04, 2020.

(online platform ZOOM)

Lecturer: Professor Daniel Alpay, Chapman University, Orange, CA, USA

Title: A Course on Positive Definite Functions and Reproducing Kernel Spaces

Abstract: Positive definite functions and reproducing kernel spaces play an important role in various fields of mathematics, ranging from pure analysis, to group representations, to the theory of coherent states, linear system theory, quantum mechanics and machine learning, to name a few. In the course, we will go over the main properties of positive definite functions (and of the closely related notion of conditionally negative functions), reproducing kernel spaces, and their operators, also in the indefinite metric setting. We will then:

(1) Discuss briefly some de Branges Rovnyak spaces, operator models, and their counter- parts in a variety of settings.

(2) Draw examples from hypercomplex analysis.

(3) Discuss the applications in infinite dimensional analysis and the theory of generalized stochastic processes.

All the examples will be taken from the latest developments of the theory.

Tentative schedule: (see below for a time converter)

Monday November 23,  8AM - 9:30AM or 08:00-09:30 (PST)

Wednesday November 25,  8AM - 9:30AM or 08:00-09:30 (PST)

Monday November 30,  8AM - 9:30AM or 08:00-09:30 (PST)

Wednesday December 02,  8AM - 9:30AM or 08:00-09:30 (PST)

Friday December 04,  8AM - 9:30AM or 08:00-09:30 (PST)


This event is supported by the

International Society for Analysis, its Applications, and Computation