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Title: A basis in an invariant subspace of analytic functions

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.
Authors:
 [1] ;  [2]
  1. Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa (Russian Federation)
  2. Bashkir State University, Ufa (Russian Federation)
Publication Date:
OSTI Identifier:
22365851
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 204; Journal Issue: 12; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ANALYTIC FUNCTIONS; DIAGRAMS; EIGENFUNCTIONS; INTERPOLATION; LIMITING VALUES; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE