Determinantal processes and division invariant spaces

We explore the link between determinantal point processes and Hilbert spaces of functions invariant with respect to division. The class of spaces under consideration extends the classical de Branges spaces of entire functions. The spaces corresponding to determinantal processes are shown to have integrable reproducing kernel. Analytic properties of the elements of these spaces are investigated.
The talk is based on a joint work with Alexander Bufetov. The work is supported by RFBR (Russian Foundation for Basic Research, grant No 20-51-14001).
References
[1] Bufetov A., Romanov R., “Division subspaces and integrable kernels.” Bull. London Math. Soc., 51: 267–277, 2019.