Riesz property in the case of multiple eigenvalues

Boris Mityagin; Petr Siegl

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arXiv · 2605.04659

Riesz property in the case of multiple eigenvalues

Boris Mityagin·Petr Siegl

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Abstract

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 $d/2 < r < \infty$.

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Boris Mityagin, Petr Siegl. 2026-05-06. Riesz property in the case of multiple eigenvalues. https://arxiv.org/abs/2605.04659

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