Weyl’s Law
نویسنده
چکیده
These are notes for a talk given in the Student Analysis Seminar at the University of Michigan. The Laplacian on a bounded domain in Rn has a discrete set of Dirichlet eigenvalues, accumulating only at ∞. Let N(λ) be the number of eigenvalues less than λ, then Weyl’s law asserts that the first term of the asymptotic expansion of N(λ) depends only on the dimension and the volume of the domain. Here we sketch the 1912 proof of Weyl, following the expositions of [1], [5], [6].
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تاریخ انتشار 2015