This item is available under a Creative Commons License for non-commercial use only
We investigate the existence and asymptotic behaviour of higher derivatives of the spectral function in the context of one-dimensional Schr¨odinger operators on the half-line with integrable potentials. In particular, we identify sufficient conditions on the potential for the existence and continuity of the n-th derivative, and outline a systematic procedure for estimating numerical upper bounds for the turning points of such derivatives. Explicit worked examples illustrate the development and application of the theory.
Gilbert, D., Harris, B., & Richl, S. (2008). Higher Derivatives of Spectral Functions Associated with One-Dimensional Schrodinger Operators. Advances and Applications, vol. 186, no 7, pp 217-228. doi:10.1007/978-3-7643-8755-6_10