Singularities and asymptotic distribution of resonances for Schr\'odinger operators in one dimension

Autor:	Christiansen, T. J., Cunningham, T.
Rok vydání:	2023
Předmět:	Mathematical Physics Mathematics - Spectral Theory 35P25 81U24 58J50 47A40
Druh dokumentu:	Working Paper
Popis:	We obtain new results about the high-energy distribution of resonances for the one-dimensional Schr\"odinger operator. Our primary result is an upper bound on the density of resonances above any logarithmic curve in terms of the singular support of the potential. We also prove results about the distribution of resonances in sectors away from the real axis, and construct a class of potentials producing multiple sequences of resonances along distinct logarithmic curves, explicitly calculating the asymptotic location of these resonances. The results are unified by the use of an integral representation of the reflection coefficients. Comment: 22 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2311.00804 Zobrazit plný text záznamu View this record from Arxiv