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Title: Spectral analysis of difference and differential operators in weighted spaces

This paper is concerned with describing the spectrum of the difference operator K:l{sub α}{sup p}(Z,X)→l{sub α}{sup p}(Z......athscrKx)(n)=Bx(n−1),  n∈Z,  x∈l{sub α}{sup p}(Z,X), with a constant operator coefficient B, which is a bounded linear operator in a Banach space X. It is assumed that K acts in the weighted space l{sub α}{sup p}(Z,X), 1≤p≤∞, of two-sided sequences of vectors from X. The main results are obtained in terms of the spectrum σ(B) of the operator coefficient B and properties of the weight function. Applications to the study of the spectrum of a differential operator with an unbounded operator coefficient (the generator of a strongly continuous semigroup of operators) in weighted function spaces are given. Bibliography: 23 titles.
Authors:
 [1]
  1. North-Ossetia State University, Vladikavkaz (Russian Federation)
Publication Date:
OSTI Identifier:
22365878
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 204; Journal Issue: 11; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; BANACH SPACE; FUNCTIONS; MATHEMATICAL OPERATORS; MATHEMATICAL SOLUTIONS; VECTORS