Trace formulae for the eigenvalues of the Laplacian期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Trace formulae for the eigenvalues of the Laplacian

Authors:	B. D. Sleeman E. M. E. Zayed

Affiliation:	(1) Dept. of Mathematical Sciences, University of Dundee, DD1 4HN Dundee, Scotland, UK;(2) Faculty of Science, Mathematics Dept. Zagazig University, Egypt

Abstract:	Summary The trace function $Theta (t) = sumlimits_{m = 1}^infty {exp ( - lambda _m t)}$ where {_m}_m=1 are the eigenvalues of the Laplacian is studied for a variety of domains. The dependence of(t) on the connectivity of a domain and the boundary conditions is analysed. Particular attention is given to annular domains. Résumé Pour divers domaines, on étudie la fonction trace $Theta (t) = sumlimits_{m = 1}^infty {exp ( - lambda _m t)}$ , où ₁, ₂, ₃, sont les valeurs propres du laplacien. On analyse comment(t) dépend du domaine et des conditions aux limites. On considère notamment le cas de couronnes circulaires.

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