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Mat. Sb., 2013, Volume 204, Number 11, Pages 3–20 (Mi msb8124)  

This article is cited in 8 scientific papers (total in 8 papers)

Spectral analysis of difference and differential operators in weighted spaces

M. S. Bichegkuev

North-Ossetia State University, Vladikavkaz

Abstract: This paper is concerned with describing the spectrum of the difference operator
$$ \mathscr{K}\colon l_\alpha^p(\mathbb Z,X)\to l_\alpha^p(\mathbb Z,X),\quad (\mathscr{K}x)(n)=Bx(n-1), n\in\mathbb{Z}, x\in l_\alpha^p(\mathbb Z,X), $$
with a constant operator coefficient $B$, which is a bounded linear operator in a Banach space $X$. It is assumed that $\mathscr{K}$ acts in the weighted space $l_\alpha^p(\mathbb Z,X)$, $1\leq p\leq \infty$, of two-sided sequences of vectors from $X$. The main results are obtained in terms of the spectrum $\sigma(B)$ 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.

Keywords: difference operator, differential operator, spectrum of an operator, weighted spaces of sequences and functions.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00378


DOI: https://doi.org/10.4213/sm8124

Full text: PDF file (587 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2013, 204:11, 1549–1564

Bibliographic databases:

Document Type: Article
UDC: 517.983.2
MSC: 47B39, 47B37
Received: 28.03.2012 and 26.06.2013

Citation: M. S. Bichegkuev, “Spectral analysis of difference and differential operators in weighted spaces”, Mat. Sb., 204:11 (2013), 3–20; Sb. Math., 204:11 (2013), 1549–1564

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. S. Bichegkuev, “Spectral Analysis of Differential Operators with Unbounded Operator Coefficients in Weighted Spaces of Functions”, Math. Notes, 95:1 (2014), 15–21  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. M. S. Bichegkuev, “Ob obratimosti raznostnykh otnoshenii i differentsialnykh operatorov”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2014, no. 4, 109–115  zmath  elib
    3. A. G. Baskakov, “Estimates for the Green's function and parameters of exponential dichotomy of a hyperbolic operator semigroup and linear relations”, Sb. Math., 206:8 (2015), 1049–1086  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. A. G. Baskakov, A. Yu. Duplishcheva, “Difference operators and operator-valued matrices of the second order”, Izv. Math., 79:2 (2015), 217–232  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. M. S. Bichegkuev, “Lyapunov Transformation of Differential Operators with Unbounded Operator Coefficients”, Math. Notes, 99:1 (2016), 24–36  mathnet  crossref  crossref  mathscinet  isi  elib
    6. A. G. Baskakov, V. D. Kharitonov, “Spectral Analysis of Operator Polynomials and Higher-Order Difference Operators”, Math. Notes, 101:3 (2017), 391–405  mathnet  crossref  crossref  mathscinet  isi  elib
    7. A. G. Baskakov, V. B. Didenko, “On invertibility states of differential and difference operators”, Izv. Math., 82:1 (2018), 1–13  mathnet  crossref  crossref  adsnasa  isi  elib
    8. N. B. Uskova, G. V. Garkavenko, “Teorema o rasscheplenii lineinykh operatorov i asimptotika sobstvennykh znachenii raznostnykh operatorov s rastuschim potentsialom”, Sib. zhurn. chist. i prikl. matem., 18:1 (2018), 91–106  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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