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- W4300904819 abstract "In this note we prove an analogue of the Rayleigh-Faber-Krahn inequality, that is, that the geodesic ball is a maximiser of the first eigenvalue of some convolution type integral operators, on the sphere $mathbb{S}^{n}$ and on the real hyperbolic space $mathbb{H}^{n}$. It completes the study of such question for complete, connected, simply connected Riemannian manifolds of constant sectional curvature. We also discuss an extremum problem for the second eigenvalue on $mathbb{H}^{n}$ and prove the Hong-Krahn-Szeg{o} type inequality. The main examples of the considered convolution type operators are the Riesz transforms with respect to the geodesic distance of the space." @default.
- W4300904819 created "2022-10-04" @default.
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- W4300904819 date "2016-03-24" @default.
- W4300904819 modified "2023-09-26" @default.
- W4300904819 title "On first and second eigenvalues of Riesz transforms in spherical and hyperbolic geometries" @default.
- W4300904819 doi "https://doi.org/10.48550/arxiv.1603.07781" @default.
- W4300904819 hasPublicationYear "2016" @default.
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