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

N. A. Chernyavskaya, L. A. Shuster

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)483-508
Number of pages26
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume146
Issue number3
DOIs
StatePublished - 1 Jun 2016

Keywords

  • Sturm-Liouville operator
  • compactness of resolvent
  • estimates of minimal eigenvalues

ASJC Scopus subject areas

  • Mathematics (all)

Fingerprint

Dive into the research topics of 'A criterion for compactness in Lp (R) of the resolvent of the maximal general form Sturm-Liouville operator'. Together they form a unique fingerprint.

Cite this