This article is cited 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.

UDC: 513.88

Received: 20.01.1968

 English version: Mathematical Notes, 1968, 4:3, 674–679

Bibliographic databases:

•