Asymptotic distribution of resonances for one-dimensional Schrödinger operators with compactly supported potential

The asymptotic distribution of the resonances of the Schrödinger operator, that is, the poles of the analytic continuation of the kernel of its resolvent, is under investigation. Under the assumption that the potential has compact support it is shown that the system of resonances consists of two series, located close to logarithmic curves with parameters determined by the length of the support of the potential and the orders of the zeros at its end-points. The main theorem complements and refines known results; namely, it allows the analysis of complex-valued potentials with zeros of arbitrary (not necessarily integer) tangency orders at the end-points of the support and the derivation of asymptotic formulae for such potentials with qualified estimates of the remainder term.
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