Two new Weyl-type bounds for the Dirichlet Laplacian

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dc.creatorHermi, Lotfi
dc.date2007-11-26
dc.date.accessioned2026-07-07T08:45:02Z
dc.date.available2026-07-07T08:45:02Z
dc.descriptionIn this paper, we prove two new Weyl-type upper estimates for the eigenvalues of the Dirichlet Laplacian. As a consequence, we obtain the following {\em lower} bounds for its counting function. For $\la\ge \la_1$, one has N(\la) > \dfrac{2}{n+2} \dfrac{1}{H_n} (\la-\la_1)^{n/2} \la_1^{-n/2}, and N(\la) > (\dfrac{n+2}{n+4})^{n/2} \dfrac{1}{H_n} (\la-(1+4/n) \la_1)^{n/2} \la_1^{-n/2}, where H_n=\dfrac{2 n}{j_{n/2-1,1}^2 J_{n/2}^2(j_{n/2-1,1})} is a constant which depends on $n$, the dimension of the underlying space, and Bessel functions and their zeros.
dc.description20 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0711.4067
dc.identifierhttp://arxiv.org/abs/0711.4067
dc.identifierTrans. Amer. Math. Soc. 360 (2008), 1539-1558
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142858
dc.subjectSpectral Theory
dc.subjectMathematical Physics
dc.subject35P15 (Primary); 47A75, 49R50, 58J50 (Secondary)
dc.titleTwo new Weyl-type bounds for the Dirichlet Laplacian
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