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Eigenvalues of non-selfadjoint functional difference operators

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arxiv 2504.06858 v1 pith:5RQNINOX submitted 2025-04-09 math.SP math-phmath.MP

Eigenvalues of non-selfadjoint functional difference operators

Alexei Ilyin , Ari Laptev , Lukas Schimmer , Anna Zernova This is my paper
classification math.SP math-phmath.MP
keywords complexdifferenceeigenvaluesfunctionalnon-selfadjointoperatorsapproachco-authors
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Using the well known approach developed in the papers of B. Davies and his co-authors we obtain inequalities for the location of possible complex eigenvalues of non-selfadjoint functional difference operators. When studying the sharpness of the main result we discovered that complex potentials can create resonances.

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  1. Eigenfunctions of deformed Schr\"odinger equations

    hep-th 2025-11 conditional novelty 7.0

    Explicit entire eigenfunctions are constructed for the difference operators 2Λ^N cosh(p)+V_N(x) with arbitrary polynomial potential; they become square-integrable only at a discrete set of energies.