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Spectral Theory and Differential Operators$
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David Edmunds and Des Evans

Print publication date: 2018

Print ISBN-13: 9780198812050

Published to Oxford Scholarship Online: September 2018

DOI: 10.1093/oso/9780198812050.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 18 November 2019

Global and Asymptotic Estimates for the Eigenvalues of −Δ‎ + q when q Is Real

Global and Asymptotic Estimates for the Eigenvalues of −Δ‎ + q when q Is Real

Chapter:
(p.497) 11 Global and Asymptotic Estimates for the Eigenvalues of −Δ‎ + q when q Is Real
Source:
Spectral Theory and Differential Operators
Author(s):

D. E. Edmunds

W. D. Evans

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198812050.003.0011

This chapter is devoted to the study of the Schrödinger operator −Δ‎ + q with q real, and, in particular, the distribution of its eigenvalues. A general result is established on an open subset Ω‎ of Rn using the Max–Min Principle and covering families of congruent cubes for the Dirichlet problem and a Whitney covering for the Neumann problem. The Cwikel–Lieb–Rosenbljum inequality is proved for q in Ln/2(Rn).

Keywords:   essential spectrum, singular sequence, T-compact perturbation, compact resolvent, finite-dimensional extension, direct and orthogonal sums

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