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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2024, Number 7, Pages 47–62
DOI: https://doi.org/10.26907/0021-3446-2024-7-47-62
(Mi ivm9997)
 

Investigation of the dimension of the spectral projection of a self-adjoint second order quasidifferential operator

M. Yu. Vatolkin

Kalashnikov Izhevsk State Technical University, 7 Studencheskaya str., Izhevsk, 426069 Russia
References:
Abstract: Let λ1 and λ2 be real, λ1<λ2, functions ψ(λi,t) be solutions to the second order quasidifferential equations Lψ=λi0Pψ, i=1,2, satisfying a homogeneous boundary condition at point a. We express the number of eigenvalues of operator L, belonging to the interval (λ1,λ2) (or the dimension of its spectral projection relative to the interval (λ1,λ2)), in terms of the number of zeros of the Vronskian composed for the functions ψ(λ1,t) and ψ(λ2,t).
Keywords: quasidifferential operator, spectral projection, self-adjoint quasidifferential expression.
Received: 01.06.2023
Revised: 06.12.2023
Accepted: 26.12.2023
Bibliographic databases:
Document Type: Article
UDC: 517.925
Language: Russian
Citation: M. Yu. Vatolkin, “Investigation of the dimension of the spectral projection of a self-adjoint second order quasidifferential operator”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 7, 47–62
Citation in format AMSBIB
\Bibitem{Vat24}
\by M.~Yu.~Vatolkin
\paper Investigation of the dimension of the spectral projection of a self-adjoint second order quasidifferential operator
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2024
\issue 7
\pages 47--62
\mathnet{http://mi.mathnet.ru/ivm9997}
\crossref{https://doi.org/10.26907/0021-3446-2024-7-47-62}
\edn{https://elibrary.ru/CPLJVX}
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    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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