Riesz property in the case of multiple eigenvalues
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910194369298432 |
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| author | Mityagin, Boris Siegl, Petr |
| author_facet | Mityagin, Boris Siegl, Petr |
| contents | We analyze spectra and the Riesz property of spectral projections of non-symmetric perturbations of self-adjoint operators with eigenvalues having arbitrary multiplicities, including infinite ones. In particular, we establish the Riesz property for perturbations of the multi-dimensional harmonic oscillator, Landau Hamiltonian and Laplace-Beltrami operator on a sphere by complex-valued $L^r$-potentials if $d/2 < r < \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04659 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Riesz property in the case of multiple eigenvalues Mityagin, Boris Siegl, Petr Spectral Theory Mathematical Physics Analysis of PDEs Functional Analysis 47A10, 47A55, 47A70, 47A75, 35P10, 35P15, 35J10, 81Q12 We analyze spectra and the Riesz property of spectral projections of non-symmetric perturbations of self-adjoint operators with eigenvalues having arbitrary multiplicities, including infinite ones. In particular, we establish the Riesz property for perturbations of the multi-dimensional harmonic oscillator, Landau Hamiltonian and Laplace-Beltrami operator on a sphere by complex-valued $L^r$-potentials if $d/2 < r < \infty$. |
| title | Riesz property in the case of multiple eigenvalues |
| topic | Spectral Theory Mathematical Physics Analysis of PDEs Functional Analysis 47A10, 47A55, 47A70, 47A75, 35P10, 35P15, 35J10, 81Q12 |
| url | https://arxiv.org/abs/2605.04659 |