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The asymptotic form of the spectral function in Sturm–Liouville problems with a large potential like −xc (c ≦ 2)

Published online by Cambridge University Press:  14 November 2011

M. S. P. Eastham
M. S. P. Eastham*
Affiliation:
Department of Computer Science, University of Wales, Cardiff, U.K.
*
*Author's correspondence address: 4 Howard Road, Bridport, Dorset DT6 4SH, U.K.
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Extract

A new formula is given for the spectral function in singular Sturm–Liouville problems where the potential is like – (const.)xc (0 < c ≦ 2). The formula is used to answer an open question concerning the asymptotic form of the spectral function.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 1 , 1998 , pp. 37 - 45
Copyright
Copyright © Royal Society of Edinburgh 1998

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