Measures on double or resonant eigenvalues for linear Schrödinger operator
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In this paper, the authors considered linear Schrodinger operator with double or resonant eigenvalues and derived the bound of the measure of the potentials leading to such double eigen values.About:
This article is published in Journal of Functional Analysis.The article was published on 2008-03-01 and is currently open access. It has received 1 citations till now. The article focuses on the topics: Operator (physics) & Spectrum of a matrix.read more
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Book ChapterDOI
Oscillatory Limits with Changing Eigenvalues: A Formal Study
TL;DR: In this paper, the authors deal with oscillatory limits with changing eigenvalues, more precisely with possibly crossing eigen values in space dimension greater than 1. The goal being to underline the various difficulties, to analyze them formally and present some related mathematical results obtained recently by the authors.
References
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Book
Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
Journal ArticleDOI
Unique continuation and absence of positive eigenvalues for Schrodinger operators
TL;DR: In this paper, a propriete de prolongement unique est vraie pour V∈L loc n/2 (R n ) dans l'espace de Sobolev H loc 2,q(R n) avec q=2n/(n+2)
Book
Introduction to spectral theory : with applications to Schrödinger operators
TL;DR: The spectrum of linear operators and Hilbert spaces has been studied extensively in the theory of quantum resonance as discussed by the authors, including the spectrum of Schrodinger operators and their application to locally compact operators.
Journal ArticleDOI
KAM for the nonlinear Schrödinger equation
L. Hakan Eliasson,Sergei Kuksin +1 more
TL;DR: In this paper, a KAM-theory was proposed for the Schrodinger equation under periodic boundary conditions, in which a large subset of the domain is sufficiently small, such that for all ε ≥ 0, the solution of ε is a time-quasi-periodic solution with all Lyapounov exponents equal to zero and whose linearized equation is reducible to constant coefficients.