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Title: On spectral synthesis on zero-dimensional Abelian groups

Let G be a zero-dimensional locally compact Abelian group all of whose elements are compact, and let C(G) be the space of all complex-valued continuous functions on G. A closed linear subspace H⊆C(G) is said to be an invariant subspace if it is invariant with respect to the translations τ{sub y}:f(x)↦f(x+y), y∈G. In the paper, it is proved that any invariant subspace H admits spectral synthesis, that is, H coincides with the closed linear span of the characters of G belonging to H. Bibliography: 25 titles.
Authors:
 [1]
  1. Petrozavodsk State University, Petrozavodsk (Russian Federation)
Publication Date:
OSTI Identifier:
22365970
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 204; Journal Issue: 9; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; FUNCTIONS; GROUP THEORY; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; SPACE; TRANSFORMATIONS