Spectral convergence of high-dimensional spheres to Gaussian spaces
Asuka Takatsu
Tokyo Metropolitan University; RIKEN Center for Advanced Intelligence Project (AIP), Tokyo, Japan
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Abstract
We prove that the spectral structure on the -dimensional standard sphere of radius compatible with a projection onto the first -coordinates converges to the spectral structure on the -dimensional Gaussian space with variance 1 as . We also show the analogue for the first Dirichlet eigenvalue problem on a ball in the sphere and that on a halfspace in the Gaussian space.
Cite this article
Asuka Takatsu, Spectral convergence of high-dimensional spheres to Gaussian spaces. J. Spectr. Theory 12 (2022), no. 4, pp. 1317–1346
DOI 10.4171/JST/424