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Izv. RAN. Ser. Mat., 2018, Volume 82, Issue 1, Pages 3–16 (Mi izv8543)  

This article is cited in 3 scientific papers (total in 3 papers)

On invertibility states of differential and difference operators

A. G. Baskakov, V. B. Didenko

Voronezh State University

Abstract: To every differential operator with unbounded operator coefficients we assign a difference operator in a space of bounded sequences. We prove the coincidence of the invertibility states of these operators (this means that the properties of the images and kernels of these operators coincide). We give a general scheme for proving the coincidence of the invertibility states of two abstract operators.

Keywords: invertibility states, Fredholm property, family of evolution operators, differential operator, difference operator.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.3464.2017/4.6
Russian Foundation for Basic Research 16-01-00197
The work of the first author, including Theorem 10, was supported by the Ministry of Science and Education of Russia in the framework of the project part (project no. 1.3464.2017/4.6). That of the second was supported by the Russian Foundation for Basic Research (project no. 16-01-00197).


DOI: https://doi.org/10.4213/im8543

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English version:
Izvestiya: Mathematics, 2018, 82:1, 1–13

Bibliographic databases:

UDC: 517.937+517.983
MSC: 34G10, 46B45, 47A53, 47B39
Received: 10.03.2016

Citation: A. G. Baskakov, V. B. Didenko, “On invertibility states of differential and difference operators”, Izv. RAN. Ser. Mat., 82:1 (2018), 3–16; Izv. Math., 82:1 (2018), 1–13

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/izv/v82/i1/p3

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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. D. B. Didenko, “Spectral Properties of the Operators $AB$ and $BA$”, Math. Notes, 103:2 (2018), 196–208  mathnet  crossref  crossref  isi  elib
    2. A. G. Baskakov, L. Yu. Kabantsova, T. I. Smagina, “Invertibility conditions for second-order differential operators in the space of continuous bounded functions”, Differ. Equ., 54:3 (2018), 285–294  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    3. A. G. Baskakov, N. B. Uskova, “Spectral analysis of differential operators with involution and operator groups”, Differ. Equ., 54:9 (2018), 1261–1265  crossref  crossref  isi  elib  scopus
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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