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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

Representation of functions in an invariant subspace with almost real spectrum


Authors: O. A. Krivosheeva and A. S. Krivosheev
Translated by: E. Peller
Original publication: Algebra i Analiz, tom 29 (2017), nomer 4.
Journal: St. Petersburg Math. J. 29 (2018), 603-641
MSC (2010): Primary 30B50
DOI: https://doi.org/10.1090/spmj/1509
Published electronically: June 1, 2018
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Abstract: The invariant subspaces with almost real spectrum are studied. By a method based on the Leont'ev interpolation function, a criterion of the fundamental principle is obtained for these spaces. This criterion only consists of a simple geometric condition on the local distribution of the points of the spectrum with multiplicities. A complete characterization is given for the space of coefficients of the series that represent functions in an invariant subspace.


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Additional Information

O. A. Krivosheeva
Affiliation: Bashkir State University, Zaki Validi street 32, 450076 Ufa, Russia
Email: kriolesya2006@yandex.ru

A. S. Krivosheev
Affiliation: Institute of Mathematics with Computing Center of Ufa Scientific Center, Russian Academy of Sciences, Chernyshevsky street 112, 450048 Ufa, Russia

DOI: https://doi.org/10.1090/spmj/1509
Keywords: Almost real spectrum, invariant subspace, entire function, basis
Received by editor(s): March 5, 2016
Published electronically: June 1, 2018
Article copyright: © Copyright 2018 American Mathematical Society

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