Uniform resolvent estimates and absence of eigenvalues of biharmonic operators with complex potentials
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915136319520768 |
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| author | Cossetti, Lucrezia Fanelli, Luca Krejcirik, David |
| author_facet | Cossetti, Lucrezia Fanelli, Luca Krejcirik, David |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06823 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniform resolvent estimates and absence of eigenvalues of biharmonic operators with complex potentials Cossetti, Lucrezia Fanelli, Luca Krejcirik, David Analysis of PDEs Spectral Theory 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. |
| title | Uniform resolvent estimates and absence of eigenvalues of biharmonic operators with complex potentials |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2309.06823 |