The International Intensive Courses dedicated to Dirac operators, Hypercomplex and Harmonic Analysis are jointly organized by Chapman University, Politecnico di Milano, and the University of Aveiro and supported by the ISAAC society. This 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 the field of Dirac operators, Hypercomplex and Harmonic Analysis. For details consult the webpage
The first edition will be a course on Reproducing Kernel Spaces lectured by Professor Daniel Alpay, from Chapman University. The course will take place online, from November 23 to December 04, 2020. The details will be provided and posted in due time.
Persons interested in participating are kindly requested to register by sending an e-mail to
no later than November 16, 2020.
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 conditonally 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 counterparts 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.