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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
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
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
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https://www.mathnet.ru/eng/ivm9997 https://www.mathnet.ru/eng/ivm/y2024/i7/p47
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Abstract page: | 59 | Full-text PDF : | 3 | References: | 15 | First page: | 7 |
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