Method of Similar Operators in the Study of Spectral Properties of Perturbed First-Order Differential Operators

In this paper, we consider first-order differential operators with periodic boundary conditions acting in a Hilbert space of square summable functions on the segment [0 , ω ] perturbed by Hilbert– Schmidt integral operators. A similarity transformation of the original operator to the operator of the...

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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 263; no. 5; pp. 599 - 615
Main Authors Baskakov, A. G., Krishtal, I. A., Uskova, N. B.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2022
Springer
Springer Nature B.V
Subjects
Boundary conditions
Differential equations
Hilbert space
Mathematics
Mathematics and Statistics
Operators (mathematics)
37K35
spectrum
35Q53
method of similar operators
37K10
integro-differential operator
35L75
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-022-05952-3

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Summary:In this paper, we consider first-order differential operators with periodic boundary conditions acting in a Hilbert space of square summable functions on the segment [0 , ω ] perturbed by Hilbert– Schmidt integral operators. A similarity transformation of the original operator to the operator of the block-diagonal structure is performed; this allows one to study spectral properties of the perturbed operator. The research method is the method of similar operators, which also presented in this work.
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05952-3