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Asymptotic behavior on (−∞, 0) of the spectral measures of a family of singular Sturm-Liouville operators

Asymptotic behavior on (−∞, 0) of the spectral measures of a family of singular Sturm-Liouville... We find the asymptotics as λ/ɛ → −∞ of the density of the spectral measure of the Sturm-Liouville operator in L 2(0,+∞) generated by the expression −y″ + ɛq(x)y, ɛ > 0, with the boundary condition y(0) cos α+y′(0) sinα = 0. The potential q(x) tends to −∞ as x → +∞ and is assumed to satisfy the Sears condition and some additional regularity conditions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Asymptotic behavior on (−∞, 0) of the spectral measures of a family of singular Sturm-Liouville operators

Differential Equations , Volume 45 (6) – Jul 19, 2009

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References (6)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Pleiades Publishing, Ltd.
Subject
Mathematics; Difference and Functional Equations; Partial Differential Equations; Ordinary Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266109060044
Publisher site
See Article on Publisher Site

Abstract

We find the asymptotics as λ/ɛ → −∞ of the density of the spectral measure of the Sturm-Liouville operator in L 2(0,+∞) generated by the expression −y″ + ɛq(x)y, ɛ > 0, with the boundary condition y(0) cos α+y′(0) sinα = 0. The potential q(x) tends to −∞ as x → +∞ and is assumed to satisfy the Sears condition and some additional regularity conditions.

Journal

Differential EquationsSpringer Journals

Published: Jul 19, 2009

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