Faculty Publications

Title

Higher derivatives of spectral functions associated with one-dimensional schrödinger operators

Document Type

Article

Keywords

Spectral functions, Sturm-liouville problems, Unbounded selfadjoint operators

Journal/Book/Conference Title

Operator Theory: Advances and Applications

Volume

186

First Page

217

Last Page

228

Abstract

We investigate the existence and asymptotic behaviour of higher derivatives of the spectral function, p(λ), on the positive real axis, in the context of one-dimensional Schrödinger operators on the half-line with integrable potentials. In particular, we identify sufficient conditions on the potential for the existence and continuity of the nth derivative, p (n) (λ), and outline a systematic procedure for estimating numerical upper bounds for the turning points of such derivatives. The potential relevance of our results to some topical issues in spectral theory is discussed.

Original Publication Date

1-1-2009

DOI of published version

10.1007/978-3-7643-8755-6_10

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