Uniform resolvent estimates and absence of eigenvalues of biharmonic operators with complex potentials

We quantify the subcriticality of the bilaplacian in dimensions greater than four by providing explicit repulsivity/smallness conditions on complex additive perturbations under which the spectrum remains stable. Our assumptions cover critical Rellich-type potentials too. As a byproduct we obtain uni...

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Bibliographic Details
Published inJournal of functional analysis Vol. 287; no. 12; p. 110646
Main Authors Cossetti, Lucrezia, Fanelli, Luca, Krejčiřík, David
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.12.2024
Subjects
Biharmonic operators
Non-self-adjoint operators
Spectral stability
Spectral stability
Biharmonic operators
Non-self-adjoint operators
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Summary:We quantify the subcriticality of the bilaplacian in dimensions greater than four by providing explicit repulsivity/smallness conditions on complex additive perturbations under which the spectrum remains stable. Our assumptions cover critical Rellich-type potentials too. As a byproduct we obtain uniform resolvent estimates in weighted spaces. Some of the results are new also in the self-adjoint setting.
ISSN:0022-1236
DOI:10.1016/j.jfa.2024.110646