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Mat. Zametki, 2011, Volume 89, Issue 2, Pages 226–240 (Mi mz6612)  

This article is cited in 9 scientific papers (total in 9 papers)

On the Spectral Properties of Differential Operators with Unbounded Operator Coefficients Determined by a Linear Relation

V. B. Didenko

Voronezh State University

Abstract: Necessary and sufficient conditions for the invertibility and the Fredholm property of operators generated by a family of evolution operators and by the boundary conditions determined by a linear relation are obtained.

Keywords: linear relation, invertibility, Fredholm property, Banach space, Banach algebra, evolution operator, Fredholm relation, resolvent set

DOI: https://doi.org/10.4213/mzm6612

Full text: PDF file (508 kB)
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English version:
Mathematical Notes, 2011, 89:2, 224–237

Bibliographic databases:

UDC: 517
Received: 13.01.2009

Citation: V. B. Didenko, “On the Spectral Properties of Differential Operators with Unbounded Operator Coefficients Determined by a Linear Relation”, Mat. Zametki, 89:2 (2011), 226–240; Math. Notes, 89:2 (2011), 224–237

Citation in format AMSBIB
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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. V. B. Didenko, “On the continuous invertibility and the Fredholm property of differential operators with multi-valued impulse effects”, Izv. Math., 77:1 (2013), 3–19  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. G. Baskakov, “Analysis of linear differential equations by methods of the spectral theory of difference operators and linear relations”, Russian Math. Surveys, 68:1 (2013), 69–116  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. V. B. Didenko, “O sostoyaniyakh obratimosti lineinykh differentsialnykh operatorov s neogranichennymi periodicheskimi koeffitsientami”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:2 (2014), 136–144  mathnet
    4. V. M. Bruk, “Dissipative expansions of a symmetric relation generated by a system of integral equations with operator measures”, Russian Math. (Iz. VUZ), 58:12 (2014), 7–22  mathnet  crossref
    5. V. M. Bruk, “Invertibility of linear relations generated by integral equation with operator measures”, Ufa Math. J., 6:4 (2014), 48–59  mathnet  crossref
    6. 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
    7. Baskakov A.G. Didenko V.B., “Spectral Analysis of Differential Operators With Unbounded Periodic Coefficients”, Differ. Equ., 51:3 (2015), 325–341  crossref  mathscinet  zmath  isi  elib  scopus
    8. 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
    9. D. B. Didenko, “Spectral Properties of the Operators $AB$ and $BA$”, Math. Notes, 103:2 (2018), 196–208  mathnet  crossref  crossref  isi  elib
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