JournalsjstVol. 13, No. 4pp. 1345–1391

Lieb–Thirring and Jensen sums for non-self-adjoint Schrödinger operators on the half-line

  • Leonid Golinskii

    B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine

  • Alexei Stepanenko

    Cardiff University, Wales, UK; University of Cambridge, UK
Lieb–Thirring and Jensen sums for non-self-adjoint Schrödinger operators on the half-line cover
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Abstract

We prove upper and lower bounds for sums of eigenvalues of Lieb–Thirring type for non-self-adjoint Schrödinger operators on the half-line. The upper bounds are established for general classes of integrable potentials and are shown to be optimal in various senses by proving the lower bounds for specific potentials. We consider sums that correspond to both the critical and non-critical cases.

Cite this article

Leonid Golinskii, Alexei Stepanenko, Lieb–Thirring and Jensen sums for non-self-adjoint Schrödinger operators on the half-line. J. Spectr. Theory 13 (2023), no. 4, pp. 1345–1391

DOI 10.4171/JST/489