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This article is cited in 7 scientific papers (total in 7 papers)
On the spectrum of a class of differential operators and some imbedding theorems
O. D. Apyshev, M. Otelbaev
Abstract:
The spectral properties of the operator
$$
Lu=\frac{(-1)^{n+k}}{\rho(t)}\biggl(\frac{u(t)}{\rho(t)}\biggr)^{(2n+2k)}+\frac{(-1)^k}{\rho(t)}\biggl(V^2(t)\biggl(\frac{u(t)}{\rho(t)}\biggr)^{\!(k)}\biggr)^{\!(k)}\qquad(n,k\geqslant1)
$$
are considered. A criterion for the nuclearity of the resolvent, two-sided estimates of the nuclear norm, Green's functions on the diagonal and the norms of the inverse operator are obtained.
Bibliography: 21 titles.
Received: 19.09.1978
Citation:
O. D. Apyshev, M. Otelbaev, “On the spectrum of a class of differential operators and some imbedding theorems”, Izv. Akad. Nauk SSSR Ser. Mat., 43:4 (1979), 739–764; Math. USSR-Izv., 15:1 (1980), 1–24
Linking options:
https://www.mathnet.ru/eng/im1729https://doi.org/10.1070/IM1980v015n01ABEH001190 https://www.mathnet.ru/eng/im/v43/i4/p739
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Abstract page: | 379 | Russian version PDF: | 120 | English version PDF: | 15 | References: | 67 | First page: | 1 |
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