About the almost everywhere convergence of the spectral expansions of functions from $L_1^\a(S^N)$

Details About the almost everywhere convergence of the spectral expansions of functions from $L_1^\a(S^N)$ About the almost everywhere convergence of the spectral expansions of functions from $L_1^\a(S^N)$

2008-06-29

arxiv.org/abs/0806.4761v1

Mathematics

Functional Analysis

7 pages

Scientific paper

In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the Laplace-Beltrami 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 $L_1^\a$ is used. For the orders of Riesz means, which greater than critical index $\frac{N-1}{2}$ we proved the positive results on summability of Fourier-Laplace series. Note that when order $\alpha$ of Riesz means is less than critical index then for establish of the almost everywhere convergence requests to use other methods form proving negative results. We have constructed different method of summability of Laplace series, which based on spectral expansions property of self-adjoint Laplace-Beltrami operator on the unit sphere.

Affiliated with

Also associated with

No associations

Rating

About the almost everywhere convergence of the spectral expansions of functions from $L_1^\a(S^N)$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with About the almost everywhere convergence of the spectral expansions of functions from $L_1^\a(S^N)$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and About the almost everywhere convergence of the spectral expansions of functions from $L_1^\a(S^N)$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-259284