Higher derivatives of spectral functions associated with one-dimensional schrödinger operators
Spectral functions, Sturm-liouville problems, Unbounded selfadjoint operators
Operator Theory: Advances and Applications
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
DOI of published version
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.