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On the location of spectral concentration for Sturm–Liouville problems with rapidly decaying potential

Part of: Boundary value problems

Published online by Cambridge University Press:  26 February 2010

M. S. P. Eastham
M. S. P. Eastham
Affiliation:
Department of Computer Science, Cardiff University of Wales, P.O. Box 916, Cardiff CF2 3XF
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Extract

The spectral function ρα(μ) (−∞<μ<∞) associated with the Sturm–Liouville equation

and a boundary condition

is a non-decreasing function of μ which is defined in terms of the Titchmarsh–Weyl function mα(λ) for (1.1) and (1.2). Thus, taking into account a standardization of the sign attached to mα(λ), we have

[4, Chapter 9, Theorem 3.1; 9, Section 2.3; 21, Sections 3.3 and 6.7].

MSC classification

Secondary: 34B24: Sturm-Liouville theory
Type
Research Article
Information
Mathematika , Volume 45 , Issue 1 , June 1998 , pp. 25 - 36
Copyright
Copyright © University College London 1998

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