Abstract:
In this note we prove that the reproducing kernel of a Hilbert space satisfying the division property has integrable form, is locally of trace class, and the Hilbert space itself is a Hilbert space of holomorphic functions.
The research of A. Bufetov on this project has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 647133
(ICHAOS). A. Bufetov has also been funded by RFBR grant 18-31-20031 and the grant MD 5991.2016.1 of the
President of the Russian Federation, by the Russian Academic Excellence Project ‘5-100’ and by the Chaire
Gabriel Lamé at the Chebyshev Laboratory of the SPbSU, a joint initiative of the French Embassy in the
Russian Federation and the Saint-Petersburg State University. The work of R. Romanov was supported by the
Russian Science Foundation Grant 17-11-01064 (Theorems 3.1 and 3.5).
This publication is cited in the following 3 articles:
Roman Romanov, “Functional Description of a Class of Quasi-Invariant Determinantal Processes”, Ann. Henri Poincaré, 2024
A. Bufetov, A. I. Bufetov, “A Palm hierarchy for determinantal point processes with the confluent hypergeometric kernel, which resolves the problem of harmonic analysis on the infinite-dimensional unitary group”, St. Petersburg Math. J., 35:5 (2024), 769
Alexander I. Bufetov, Andrey V. Dymov, Hirofumi Osada, “The logarithmic derivative for point processes with equivalent Palm measures”, J. Math. Soc. Japan, 71:2 (2019), 451–469
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