Spectral Analysis of Differential Operators with Unbounded Operator Coefficients in Weighted Spaces of Functions

被引：5

作者：

Bichegkuev, M. S. ^{[1
]}

机构：

[1] North Ossetian State Univ, Vladikavkaz, Russia

来源：

MATHEMATICAL NOTES | 2014年 / 95卷 / 1-2期

基金：

俄罗斯基础研究基金会;

关键词：

differential operator; weighted spaces of functions; spectral properties of operators; evolution operator; exponential dichotomy; Howland difference operator; Banach space; spectrum mapping theorem; SEMIGROUPS; EQUATIONS;

D O I：

10.1134/S0001434614010027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The spectral properties of operators constructed from a family of evolution operators are studied in Banach spaces of vector functions defined by a weight function of pre-exponential growth. Necessary and sufficient conditions for the invertibility of such operators are obtained in terms of exponential dichotomy. We prove a spectrum mapping theorem for semigroups of Howland difference operators generated by the operator under study.

引用

页码：15 / 21

页数：7

共 14 条

[1] Analysis of linear differential equations by methods of the spectral theory of difference operators and linear relations
Baskakov, A. G.
[J]. RUSSIAN MATHEMATICAL SURVEYS, 2013, 68 (01) : 69 - 116
[2] Spectral analysis of differential operators with unbounded operator-valued coefficients, difference relations and semigroups of difference relations
Baskakov, A. G.
[J]. IZVESTIYA MATHEMATICS, 2009, 73 (02) : 215 - 278
[3] Representation theory for Banach algebras, Abelian groups, and semigroups in the spectral analysis of linear operators
Baskakov A.G.
[J]. Journal of Mathematical Sciences, 2006, 137 (4) : 4885 - 5036
[4] On correct linear differential operators
Baskakov, AG
[J]. SBORNIK MATHEMATICS, 1999, 190 (3-4) : 323 - 348
[5] Linear differential operators with unbounded operator coefficients and semigroups of bounded operators
Baskakov, AG
[J]. MATHEMATICAL NOTES, 1996, 59 (5-6) : 586 - 593
[6] Semigroups of difference operators in spectral analysis of linear differential operators
Baskakov, AG
[J]. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1996, 30 (03) : 149 - 157
[7] Spectral analysis of difference and differential operators in weighted spaces
Bichegkuev, M. S.
[J]. SBORNIK MATHEMATICS, 2013, 204 (11) : 1549 - 1564
[8] On conditions for invertibility of difference and differential operators in weight spaces
Bichegkuev, M. S.
[J]. IZVESTIYA MATHEMATICS, 2011, 75 (04) : 665 - 680
[9] Solvability conditions for the difference equations with an initial condition in a subspace
Bichegkuev, M. S.
[J]. SIBERIAN MATHEMATICAL JOURNAL, 2010, 51 (04) : 595 - 609
[10] On the spectrum of difference and differential operators in weighted spaces
Bichegkuev, M. S.
[J]. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2010, 44 (01) : 65 - 68

← 1 2 →