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Bull. Lond. Math. Soc., 2019, Volume 51, Issue 2, Pages 267–277 (Mi blms4)  

Division subspaces and integrable kernels

A. I. Bufetovab, R. V. Romanovcd

a CNRS, Centrale Marseille, Institut de Mathématiques de Marseille, Aix-Marseille Université UMR7373, 39 Rue F. Joliot Curie 13453, Marseille, France
b Steklov Institute of Mathematics, Moscow 119991, Russia
c Faculty of Physics and Engineering, ITMO University, Saint-Petersburg 197101, Russia
d Department of Physics, Saint-Petersburg State University, Saint-Petersburg 199034, Russia

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.

Funding Agency Grant Number
European Research Council
647133
Russian Foundation for Basic Research 18-31-20031
Ministry of Education and Science of the Russian Federation MD 5991.2016.1
Russian Science Foundation 17-11-01064
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).


DOI: https://doi.org/10.1112/blms.12223


Bibliographic databases:

ArXiv: 1707.03463
MSC: 60G55, 46E22, 47B32
Received: 20.06.2018
Revised: 15.09.2018
Language:

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