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Mat. Sb., 2013, Volume 204, Number 12, Pages 49–104 (Mi msb8172)  

This article is cited in 7 scientific papers (total in 7 papers)

A basis in an invariant subspace of analytic functions

A. S. Krivosheeva, O. A. Krivosheevab

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa
b Bashkir State University, Ufa

Abstract: The existence problem for a basis in a differentiation-invariant subspace of analytic functions defined in a bounded convex domain in the complex plane is investigated. Conditions are found for the solvability of a certain special interpolation problem in the space of entire functions of exponential type with conjugate diagrams lying in a fixed convex domain. These underlie sufficient conditions for the existence of a basis in the invariant subspace. This basis consists of linear combinations of eigenfunctions and associated functions of the differentiation operator, whose exponents are combined into relatively small clusters. Necessary conditions for the existence of a basis are also found. Under a natural constraint on the number of points in the groups, these coincide with the sufficient conditions. That is, a criterion is found under this constraint that a basis constructed from relatively small clusters exists in an invariant subspace of analytic functions in a bounded convex domain in the complex plane.
Bibliography: 25 titles.

Keywords: interpolation, exponential polynomial, invariant subspace, basis.

Funding Agency Grant Number
Russian Foundation for Basic Research 10-01-00233-а
Ministry of Education and Science of the Russian Federation 14.В37.21.0358

Author to whom correspondence should be addressed


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English version:
Sbornik: Mathematics, 2013, 204:12, 1745–1796

Bibliographic databases:

UDC: 517.537.7
MSC: 30D15, 46E15
Received: 31.08.2012 and 05.04.2013

Citation: A. S. Krivosheev, O. A. Krivosheeva, “A basis in an invariant subspace of analytic functions”, Mat. Sb., 204:12 (2013), 49–104; Sb. Math., 204:12 (2013), 1745–1796

Citation in format AMSBIB
\by A.~S.~Krivosheev, O.~A.~Krivosheeva
\paper A basis in an invariant subspace of analytic functions
\jour Mat. Sb.
\yr 2013
\vol 204
\issue 12
\pages 49--104
\jour Sb. Math.
\yr 2013
\vol 204
\issue 12
\pages 1745--1796

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    This publication is cited in the following articles:
    1. A. S. Krivosheev, O. A. Krivosheyeva, “A basis in invariant subspace of entire functions”, St. Petersburg Math. J., 27:2 (2016), 273–316  mathnet  crossref  mathscinet  isi  elib
    2. A. S. Krivosheev, O. A. Krivosheeva, “Fundamental Principle and a Basis in Invariant Subspaces”, Math. Notes, 99:5 (2016), 685–696  mathnet  crossref  crossref  mathscinet  isi  elib
    3. O. A. Krivosheyeva, A. S. Krivosheyev, “A representation of functions from an invariant subspace with almost real spectrum”, St. Petersburg Math. J., 29:4 (2018), 603–641  mathnet  crossref  mathscinet  isi  elib
    4. O. A. Krivosheeva, “Invariant subspaces with zero density spectrum”, Ufa Math. J., 9:3 (2017), 100–108  mathnet  crossref  isi  elib
    5. O. A. Krivosheeva, “Basis in invariant subspace of analytical functions”, Ufa Math. J., 10:2 (2018), 58–77  mathnet  crossref  isi
    6. Krivosheev A., Krivosheeva O., “Representation of Analytic Functions By Series of Exponential Monomials in Convex Domains and Its Applications”, Lobachevskii J. Math., 40:9, SI (2019), 1330–1354  crossref  mathscinet  zmath  isi
    7. A. S. Krivosheev, O. A. Krivosheeva, “Invariant subspaces in half-plane”, Ufa Math. J., 12:3 (2020), 30–43  mathnet  crossref
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