Spectral properties of the logarithmic Laplacian

Ari Laptev; Tobias Weth

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arXiv · 2009.03395

Spectral properties of the logarithmic Laplacian

Ari Laptev·Tobias Weth

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Abstract

We obtain spectral inequalities and asymptotic formulae for the discrete spectrum of the operator $\frac12\, \log(-\Delta)$ in an open set $\Omega\in\Bbb R^d$, $d\ge2$, of finite measure with Dirichlet boundary conditions. We also derive some results regarding lower bounds for the eigenvalue $\lambda_1(\Omega)$ and compare them with previously known inequalities.

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Ari Laptev, Tobias Weth. 2020-09-07. Spectral properties of the logarithmic Laplacian. https://arxiv.org/abs/2009.03395

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