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

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

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English version:
Mathematical Notes, 2011, 89:2, 224–237

Bibliographic databases:

UDC: 517

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
\Bibitem{Did11} \by V.~B.~Didenko \paper On the Spectral Properties of Differential Operators with Unbounded Operator Coefficients Determined by a Linear Relation \jour Mat. Zametki \yr 2011 \vol 89 \issue 2 \pages 226--240 \mathnet{http://mi.mathnet.ru/mz6612} \crossref{https://doi.org/10.4213/mzm6612} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2840421} \transl \jour Math. Notes \yr 2011 \vol 89 \issue 2 \pages 224--237 \crossref{https://doi.org/10.1134/S0001434611010287} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000288653100028} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952404900} 

• http://mi.mathnet.ru/eng/mz6612
• https://doi.org/10.4213/mzm6612
• http://mi.mathnet.ru/eng/mz/v89/i2/p226

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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
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
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
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
5. V. M. Bruk, “Invertibility of linear relations generated by integral equation with operator measures”, Ufa Math. J., 6:4 (2014), 48–59
6. A. G. Baskakov, A. Yu. Duplishcheva, “Difference operators and operator-valued matrices of the second order”, Izv. Math., 79:2 (2015), 217–232
7. Baskakov A.G. Didenko V.B., “Spectral Analysis of Differential Operators With Unbounded Periodic Coefficients”, Differ. Equ., 51:3 (2015), 325–341
8. A. G. Baskakov, V. B. Didenko, “On invertibility states of differential and difference operators”, Izv. Math., 82:1 (2018), 1–13
9. D. B. Didenko, “Spectral Properties of the Operators $AB$ and $BA$”, Math. Notes, 103:2 (2018), 196–208
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