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Matematicheskie Zametki, 1968, Volume 4, Issue 3, Pages 301–312
(Mi mzm9451)
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This article is cited in 4 scientific papers (total in 4 papers)
Sufficient conditions that the minimum and maximum of partial differential operators should coincide and that their spectra should be discrete
M. G. Gimadislamov Fortieth Anniversary of Oktober Bashkir State University
Abstract:
An expression of the form $$ l(u)=(-1)^m\sum_{j=1}^m D_j^{2m}u+[q(x)+ir(x)]u $$ is considered. Sufficient conditions are found such that the minimum operator, formally conjugate to $l(u)$, generated by the expression and the maximum operator generated by the expression $l(u)$ in $\mathscr{L}_2(E_n)$ should coincide. It is proved that if $q(x)\to\infty$ or $q(x)+r(x)\to\infty$, $|x|\to\infty$, then the operator generated by $l(u)$ in $\mathscr{L}_2(E_n)$ has a discrete spectrum.
Received: 20.01.1968
Citation:
M. G. Gimadislamov, “Sufficient conditions that the minimum and maximum of partial differential operators should coincide and that their spectra should be discrete”, Mat. Zametki, 4:3 (1968), 301–312; Math. Notes, 4:3 (1968), 674–679
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https://www.mathnet.ru/eng/mzm9451 https://www.mathnet.ru/eng/mzm/v4/i3/p301
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Abstract page: | 141 | Full-text PDF : | 52 | First page: | 1 |
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