Hilbert Function Spaces 2025

Aim of the Conference

Hilbert and, more generally, Banach spaces of holomorphic functions have a long history. They were developed for the needs of Complex Analysis, in one and several variables, per se; then they proved to be the incubator for new theories which were landmarks of XX century mathematics. Holomorphic Hardy spaces, to mention one example, were the place where the theory of singular integrals first developed; they became, after Beurling's Invariant Space Theorem, a standard model for Operator Theory; they are the basic metaphor (and more than that) for developing the theory of martingale spaces in probability.

In the past few decades, radically new developments in Holomorphic Spaces emerged. On the one hand, they were made possible by the interdisciplinary approach to problems and objects of the theory, bringing in techniques from other mathematical fields and even from physics and engineering. On the other hand, deep connections appeared to connect seemingly far away areas of the theory and a unified approach to many different problems was possible. 

We wish to provide the right environment to substantially advance knowledge in an important field of contemporary analysis, by means of the lectures themselves, and also through the informal exchange of ideas and information, as well as through the establishment of new collaborations.

The conference aims at being the place where the worldwide community working in the area works out the “state of the art” and sets the goals for the near future. The list of the invited speakers includes most of the leading researchers, young and established, in the area of Holomorphic Spaces.