A. I. Bufetov, R. V. Romanov, “Division subspaces and integrable kernels”, Bull. Lond. Math. Soc., 2019, Volume 51, Issue 2,Pages <nobr>267–277</nobr>

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

This article is cited in 4 papers

Division subspaces and integrable kernels

A. I. Bufetov^ab, R. V. Romanov^cd

^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.

MSC: 60G55, 46E22, 47B32

Received: 20.06.2018
Revised: 15.09.2018

Language: English

DOI: 10.1112/blms.12223

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ArXiv: 1707.03463

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