1998•Proceedings of the Royal Society of Edinburgh Section A MathematicsRequires access

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

M. S. P. Eastham

Abstract

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.

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Key concepts: Sturm–Liouville theory, Spectral function, Function (biology), Mathematics, Spectral analysis, Mathematical physics, Spectral properties, Mathematical analysis