JournalsrlmVol. 31, No. 1pp. 1–13

Complex eigenvalue bounds for a Schrödinger operator on the half line

  • Francesco Ferrulli

    Imperial College London, UK
  • Ari Laptev

    Imperial College London, UK and St. Petersburg University, Russia
Complex eigenvalue bounds for a Schrödinger operator on the half line cover
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Abstract

We derive some bounds on the location of complex eigenvalues for a family of Schrödinger operators H0,νH_{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 LpL^p spaces. Some information on the geometry of the complex region which bounds the eigenvalues of the radial Schrödinger multidimensional operator are then recovered.

Cite this article

Francesco Ferrulli, Ari Laptev, Complex eigenvalue bounds for a Schrödinger operator on the half line. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 1, pp. 1–13

DOI 10.4171/RLM/876