$L^p$-Convergence of the Laplace–Beltrami Eigenfunction Expansions
C. R. Math. Rep. Acad. Sci. Canada Vol. 37 (2) 2015, pp. 76-80
June 30, 2015
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
AMS Subject Classification: Elliptic equations on manifolds; general theory 58J05
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$L^p$-Convergence of the Laplace--Beltrami Eigenfunction Expansions
