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Matematicheskie Zametki, 2014, Volume 95, Issue 1, Pages 18–25
DOI: https://doi.org/10.4213/mzm10195 (Mi mzm10195) 		 
This article is cited in 5 scientific papers (total in 5 papers)

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

M. S. Bichegkuev

North-Ossetia State University, Vladikavkaz
Full-text PDF (459 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm10195
Abstract: 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.
Keywords: differential operator, weighted spaces of functions, spectral properties of operators, evolution operator, exponential dichotomy, Howland difference operator, Banach space, spectrum mapping theorem.
Received: 19.10.2012
Revised: 08.02.2013
English version:
Mathematical Notes, 2014, Volume 95, Issue 1, Pages 15–21
DOI: https://doi.org/10.1134/S0001434614010027
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: M. S. Bichegkuev, “Spectral Analysis of Differential Operators with Unbounded Operator Coefficients in Weighted Spaces of Functions”, Mat. Zametki, 95:1 (2014), 18–25; Math. Notes, 95:1 (2014), 15–21
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    1. N. B. Uskova, “Matrichnyi analiz spektralnykh proektorov vozmuschennykh samosopryazhennykh operatorov”, Sib. elektron. matem. izv., 16 (2019), 369–405  mathnet  crossref  mathscinet
    2. A. G. Baskakov, V. B. Didenko, “On invertibility states of differential and difference operators”, Izv. Math., 82:1 (2018), 1–13  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. D. B. Didenko, “Spectral Properties of the Operators AB and BA”, Math. Notes, 103:2 (2018), 196–208  mathnet  crossref  crossref  mathscinet  isi  elib
    4. 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
    5. A. B. Antonevich, E. V. Panteleeva, “Well-Posed Boundary-Value Problems, Right Hyperbolicity, and Exponential Dichotomy”, Math. Notes, 100:1 (2016), 11–23  mathnet  crossref  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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