Rendiconti Lincei - Matematica e Applicazioni


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Volume 31, Issue 1, 2020, pp. 1–13
DOI: 10.4171/RLM/876

Published online: 2020-04-03

Complex eigenvalue bounds for a Schrödinger operator on the half line

Francesco Ferrulli[1] and Ari Laptev[2]

(1) Imperial College London, UK
(2) Imperial College London, UK and St. Petersburg University, Russia

We derive some bounds on the location of complex eigenvalues for a family of Schrödinger operators $H_{0,\nu}$ defined on the positive half line and subject to integrable complex potential. We generalise the results obtained in [14] where the operator does not have a Hardy term and also include the analysis for potentials belonging to weighted $L^p$ spaces. Some information on the geometry of the complex region which bounds the eigenvalues of the radial Schrödinger multidimensional operator are then recovered.

Keywords: Schrödinger operator, complex potential, eigenvalue bounds

Ferrulli Francesco, Laptev Ari: Complex eigenvalue bounds for a Schrödinger operator on the half line. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), 1-13. doi: 10.4171/RLM/876