Mathematical Reports - Comptes rendus mathématiques

of the Academy of Science | de l'Académie des sciences

Mathematical Reports
Comptes rendus mathématiques

of the Academy of Science | de l'Académie des sciences

eigenfunction expansion — 1 articles found.

$L^p$-Convergence of the Laplace–Beltrami Eigenfunction Expansions

C. R. Math. Rep. Acad. Sci. Canada Vol. 37 (2) 2015, pp. 76-80
Vol.37 (2) 2015
Atsushi Kanazawa Details
(Received: 2014-04-02 , Revised: 2014-07-18 )
(Received: 2014-04-02 , Revised: 2014-07-18 )

Atsushi Kanazawa,Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada; e-mail: kanazawa@10.alumni.u-tokyo.ac.jp

Abstract/Résumé:

We provide a simple sufficient condition for the \(L^p\)-convergence of the Laplace–Beltrami eigenfunction expansions of functions on a compact Riemannian manifold with a Dirichlet boundary condition.

Nous fournissons une condition suffisante simple pour la convergence \(L ^ p\) de Laplace–Beltrami expansions de fonctions sur une variété riemannienne compacte avec une condition aux limites de Dirichlet.

Keywords: Dirichlet boundary condition, Green's function, Laplace-Beltrami operator, Lp-convergence, eigenfunction expansion

AMS Subject Classification: Elliptic equations on manifolds; general theory 58J05

PDF(click to download): $L^p$-Convergence of the Laplace--Beltrami Eigenfunction Expansions