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Title: Spectral properties of the Dirichlet operator Σ{sub i=1}{sup d}(−∂{sub i}{sup 2}){sup s} on domains in d-dimensional Euclidean space

In this article, we investigate the distribution of eigenvalues of the Dirichlet pseudo-differential operator Σ{sub i=1}{sup d}(−∂{sub i}{sup 2}){sup s}, s∈(0,1] on an open and bounded subdomain Ω⊂R{sup d} and predict bounds on the sum of the first N eigenvalues, the counting function, the Riesz means, and the trace of the heat kernel. Moreover, utilizing the connection of coherent states to the semi-classical approach of quantum mechanics, we determine the sum for moments of eigenvalues of the associated Schrödinger operator.
Authors:
 [1]
  1. Department of Mathematics, School of Sciences, University of Aegean, Karlovasi 83200, Samos (Greece)
Publication Date:
OSTI Identifier:
22217890
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 10; Other Information: (c) 2013 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; ANNIHILATION OPERATORS; DIRICHLET PROBLEM; DISTRIBUTION; EIGENFUNCTIONS; EIGENSTATES; EIGENVALUES; EUCLIDEAN SPACE; HEAT; KERNELS; QUANTUM MECHANICS; SCHROEDINGER EQUATION