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Title: A short proof of Weyl's law for fractional differential operators

We study spectral asymptotics for a large class of differential operators on an open subset of R{sup d} with finite volume. This class includes the Dirichlet Laplacian, the fractional Laplacian, and also fractional differential operators with non-homogeneous symbols. Based on a sharp estimate for the sum of the eigenvalues we establish the first term of the semiclassical asymptotics. This generalizes Weyl's law for the Laplace operator.
Authors:
 [1]
  1. Department of Physics, Princeton University, Princeton, New Jersey 08544 (United States)
Publication Date:
OSTI Identifier:
22251643
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; DIRICHLET PROBLEM; EIGENVALUES; LAPLACIAN; SEMICLASSICAL APPROXIMATION