About the asymptotic formula for spectral function of the Laplace-Beltrami operator on sphere
نویسندگان
چکیده
In this work we established asymptotical behavior for Riesz means of the spectral function of the Laplace operator on unit sphere.
منابع مشابه
About the Almost Everywhere Convergence of the Spectral Expansions of Functions
Abstract. In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the LaplaceBeltrami operator on the unit sphere. The sufficient conditions for summability is obtained. The more general properties and representation by the eigenfunctions of the Laplace-Beltrami operator of the Liouville space L 1 is used. For the orders of Riesz means...
متن کاملAsymptotic Behavior of L2-normalized Eigenfunctions of the Laplace-beltrami Operator on a Closed Riemannian Manifold
Let e(x, y, λ) be the spectral function and χλ the unit band spectral projection operator, with respect to the LaplaceBeltrami operator ∆M on a closed Riemannian manifold M . We firstly review the one-term asymptotic formula of e(x, x, λ) as λ → ∞ by Hörmander (1968) and the one of ∂ x ∂ β y e(x, y, λ)|x=y as λ → ∞ in a geodesic normal coordinate chart by the author (2004) and the sharp asympto...
متن کاملSpectral Theory for the Weil-petersson Laplacian on the Riemann Moduli Space
We study the spectral geometric properties of the scalar Laplace-Beltrami operator associated to the Weil-Petersson metric gWP on Mγ , the Riemann moduli space of surfaces of genus γ > 1. This space has a singular compactification with respect to gWP, and this metric has crossing cusp-edge singularities along a finite collection of simple normal crossing divisors. We prove first that the scalar...
متن کاملBOCHNER-RIESZ SUMMABILITY FOR ANALYTIC FUNCTIONS ON THE m-COMPLEX UNIT SPHERE AND FOR CYLINDRICALLY SYMMETRIC FUNCTIONS ON R × R ADAM SIKORA AND TERENCE TAO
We prove that spectral projections of Laplace-Beltrami operator on the m-complex unit sphere E∆ S2m−1 ([0, R)) are uniformly bounded as an operator from H(S) to L(S) for all p ∈ (1,∞). We also show that the Bochner-Riesz conjecture is true when restricted to cylindrically symmetric functions on R × R. Suppose that L is a positive definite, self-adjoint operator acting on L(X,μ), where X is a me...
متن کاملHigh-Order Regularization on Graphs
The Laplace-Beltrami operator for graphs has been been widely used in many machine learning issues, such as spectral clustering and transductive inference. Functions on the nodes of a graph with vanishing Laplacian are called harmonic functions. In differential geometry, the Laplace-de Rham operator generalizes the Laplace-Beltrami operator. It is a differential operator on the exterior algebra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008