Mathematics – Spectral Theory
Scientific paper
2007-11-26
Trans. Amer. Math. Soc. 360 (2008), 1539-1558
Mathematics
Spectral Theory
20 pages, 2 figures
Scientific paper
In 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.
No associations
LandOfFree
Two new Weyl-type bounds for the Dirichlet Laplacian 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 Two new Weyl-type bounds for the Dirichlet Laplacian, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Two new Weyl-type bounds for the Dirichlet Laplacian will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-171093