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Proceedings of the American Mathematical Society

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The discreteness of the spectrum of self-adjoint, even order, one-term, differential operators


Author: Roger T. Lewis
Journal: Proc. Amer. Math. Soc. 42 (1974), 480-482
MSC: Primary 34B25
DOI: https://doi.org/10.1090/S0002-9939-1974-0330608-8
MathSciNet review: 0330608
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Abstract: An open question which was asked by I. M. Glazman is answered. It is well known that the condition

$\displaystyle \mathop {\lim }\limits_{x \to \infty } {x^{2n - 1}}\int_x^\infty {{r^{ - 1}} = 0} $

is sufficient for the discreteness and boundedness from below of the spectrum of selfadjoint extensions of $ {( - 1)^n}{(r{y^{(n)}})^{(n)}}$. This paper shows that the condition is also necessary.

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DOI: https://doi.org/10.1090/S0002-9939-1974-0330608-8
Article copyright: © Copyright 1974 American Mathematical Society