English

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

Analysis of PDEs 2025-02-05 v1 Spectral Theory

Abstract

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.

Keywords

Cite

@article{arxiv.2309.06823,
  title  = {Uniform resolvent estimates and absence of eigenvalues of biharmonic operators with complex potentials},
  author = {Lucrezia Cossetti and Luca Fanelli and David Krejcirik},
  journal= {arXiv preprint arXiv:2309.06823},
  year   = {2025}
}