On first and second eigenvalues of Riesz transforms in spherical and hyperbolic geometries
On first and second eigenvalues of Riesz transforms in spherical and hyperbolic geometries
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 …