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Mat. Zametki, 1971, Volume 9, Issue 4, Pages 391–399 (Mi mz7018)  

A discreteness criterion for the spectrum of a quasielliptic operator

M. G. Gimadislamov

Bashkir State University

Abstract: For the spectrum of the operator
$$u=\sum_{j=1}^n{(-1)^{m_j}D_j^{2m_j}u+q(x)u},$$
to be discrete, where the mj are arbitrary positive integers such that $\sum_{j=1}^n{\frac1{2m_j}<1}$, and $q(x)\ge 1$, it is necessary and sufficient that $\int\limits_K{q(x)dx\to\infty}$ , when the cube $K$ tends to infinity while preserving its dimensions.

Full text: PDF file (487 kB)

English version:
Mathematical Notes, 1971, 9:4, 225–229

Bibliographic databases:

UDC: 513.88
Received: 24.12.1969

Citation: M. G. Gimadislamov, “A discreteness criterion for the spectrum of a quasielliptic operator”, Mat. Zametki, 9:4 (1971), 391–399; Math. Notes, 9:4 (1971), 225–229

Citation in format AMSBIB
\Bibitem{Gim71}
\by M.~G.~Gimadislamov
\paper A~discreteness criterion for the spectrum of a~quasielliptic operator
\jour Mat. Zametki
\yr 1971
\vol 9
\issue 4
\pages 391--399
\mathnet{http://mi.mathnet.ru/mz7018}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=288437}
\zmath{https://zbmath.org/?q=an:0226.35048|0216.38203}
\transl
\jour Math. Notes
\yr 1971
\vol 9
\issue 4
\pages 225--229
\crossref{https://doi.org/10.1007/BF01387769}


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