This article is cited in 10 papers

Spectral decomposition of model operators in de Branges spaces

G. M. Gubreev^a, A. A. Tarasenko<sup>b

a</sup> Poltava National Technical University named after Yuri Kondratyuk
^b Universidad Autónoma del Estado de Hidalgo

Abstract: The paper is devoted to studying a class of completely continuous nonselfadjoint operators in de Branges spaces of entire functions. Among other results, a class of unconditional bases of de Branges spaces consisting of values of their reproducing kernels is constructed. The operators that are studied are model operators in the class of completely continuous non-dissipative operators with two-dimensional imaginary parts.
Bibliography: 22 titles.

Keywords: de Branges spaces, nonselfadjoint operators, the Muckenhoupt condition, unconditional bases consisting of values of reproducing kernels.

UDC: 517.583+517.518

MSC: Primary 47B32; Secondary 30D15, 46E22, 47A10, 47A70

Received: 16.07.2009 and 24.06.2010

DOI: 10.4213/sm7603

 English version: Sbornik: Mathematics, 2010, 201:11, 1599–1634

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