Faculty Publications
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.
Department
Department of Mathematics
Original Publication Date
1-1-2009
DOI of published version
10.1007/978-3-7643-8755-6_10
Recommended Citation
Gilbert, D. J.; Harris, B. J.; and Riehl, S. M., "Higher Derivatives Of Spectral Functions Associated With One-Dimensional Schrödinger Operators" (2009). Faculty Publications. 2311.
https://scholarworks.uni.edu/facpub/2311
