A criterion for compactness in Lp (R) of the resolvent of the maximal general form Sturm-Liouville operator

N. A. Chernyavskaya; L. A. Shuster

doi:10.1017/S0308210515000694

A criterion for compactness in L_p (R) of the resolvent of the maximal general form Sturm-Liouville operator

N. A. Chernyavskaya
, L. A. Shuster

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the equation where and We assume that this equation is correctly solvable in Lp (R). Under these assumptions, we study the problem of compactness of the resolvent of the maximal continuously invertible Sturm-Liouville operator. Here In the case p = 2, for the compact operator, we obtain two-sided sharp-by-order estimates of the maximal eigenvalue.

Original language	English
Pages (from-to)	483-508
Number of pages	26
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	146
Issue number	3
DOIs	https://doi.org/10.1017/S0308210515000694
State	Published - 1 Jun 2016

Keywords

Sturm-Liouville operator
compactness of resolvent
estimates of minimal eigenvalues

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1017/S0308210515000694

Cite this

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abstract = "We consider the equation where and We assume that this equation is correctly solvable in Lp (R). Under these assumptions, we study the problem of compactness of the resolvent of the maximal continuously invertible Sturm-Liouville operator. Here In the case p = 2, for the compact operator, we obtain two-sided sharp-by-order estimates of the maximal eigenvalue.",

keywords = "Sturm-Liouville operator, compactness of resolvent, estimates of minimal eigenvalues",

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AU - Shuster, L. A.

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N2 - We consider the equation where and We assume that this equation is correctly solvable in Lp (R). Under these assumptions, we study the problem of compactness of the resolvent of the maximal continuously invertible Sturm-Liouville operator. Here In the case p = 2, for the compact operator, we obtain two-sided sharp-by-order estimates of the maximal eigenvalue.

AB - We consider the equation where and We assume that this equation is correctly solvable in Lp (R). Under these assumptions, we study the problem of compactness of the resolvent of the maximal continuously invertible Sturm-Liouville operator. Here In the case p = 2, for the compact operator, we obtain two-sided sharp-by-order estimates of the maximal eigenvalue.

KW - Sturm-Liouville operator

KW - compactness of resolvent

KW - estimates of minimal eigenvalues

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