A criterion for compactness in Lp(ℝ) of the resolvent of the maximal general form Sturm–Liouville operator
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Published:2016-04-19
Issue:3
Volume:146
Page:483-508
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ISSN:0308-2105
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Container-title:Proceedings of the Royal Society of Edinburgh: Section A Mathematics
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language:en
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Short-container-title:Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Author:
Chernyavskaya N. A.,Shuster L. A.
Abstract
We consider the equationwhere andWe 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 . HereIn the case p = 2, for the compact operator , we obtain two-sided sharp-by-order estimates of the maximal eigenvalue.
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics