高维球面到高斯空间的光谱收敛性

IF 1 3区数学 Q1 MATHEMATICS Journal of Spectral Theory Pub Date : 2021-06-17 DOI:10.4171/jst/424

Asuka Takatsu

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引用次数: 2

摘要

我们证明了与前$N$坐标上的投影兼容的半径为$（N-1）^｛1/2｝$的$N$维标准球面上的谱结构收敛于方差为$N\to\infty$的$N$维高斯空间上的光谱结构。我们还展示了第一个狄利克雷本征值及其本征函数在球面中的球和高斯空间中的半空间上的模拟。

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Spectral convergence of high-dimensional spheres to Gaussian spaces

We prove that the spectral structure on the $N$-dimensional standard sphere of radius $(N-1)^{1/2}$ compatible with a projection onto the first $n$-coordinates converges to the spectral structure on the $n$-dimensional Gaussian space with variance $1$ as $N\to \infty$. We also show the analogue for the first Dirichlet eigenvalue and its eigenfunction on a ball in the sphere and on a half-space in the Gaussian space.

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来源期刊

Journal of Spectral Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

0.00%

发文量

期刊介绍： The Journal of Spectral Theory is devoted to the publication of research articles that focus on spectral theory and its many areas of application. Articles of all lengths including surveys of parts of the subject are very welcome. The following list includes several aspects of spectral theory and also fields which feature substantial applications of (or to) spectral theory. Schrödinger operators, scattering theory and resonances; eigenvalues: perturbation theory, asymptotics and inequalities; quantum graphs, graph Laplacians; pseudo-differential operators and semi-classical analysis; random matrix theory; the Anderson model and other random media; non-self-adjoint matrices and operators, including Toeplitz operators; spectral geometry, including manifolds and automorphic forms; linear and nonlinear differential operators, especially those arising in geometry and physics; orthogonal polynomials; inverse problems.