Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: II

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) We investigate boundedness of the evolutione^sup itH^ in the sense ofL^sup 2^(^sup 3^[arrow right]L^sup 2^(^sup 3^) as well asL^sup 1^(^sup 3^[arrow right]L^sup ∞^(^sup 3^) for the non-selfadjoint operator... where [mu]>0...

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Published in:Journal d'analyse mathématique (Jerusalem) 2006-12, Vol.99 (1), p.199-248
Main Authors: Burak Erdoĝan, M., Schlag, Wilhelm
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Schlag, Wilhelm
description (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) We investigate boundedness of the evolutione^sup itH^ in the sense ofL^sup 2^(^sup 3^[arrow right]L^sup 2^(^sup 3^) as well asL^sup 1^(^sup 3^[arrow right]L^sup ∞^(^sup 3^) for the non-selfadjoint operator... where [mu]>0 andV^sub 1^, V^sub 2^ are real-valued decaying potentials. Such operators arise when linearizing a focusing NLS equation around a standing wave, and the aforementioned bounds are needed in the study of nonlinear asymptotic stability of such standing waves. We derive our results under some natural spectral assumptions (corresponding to a ground state soliton of NLS), see A1)-A4) below, but without imposing any restrictions on the edges±μ of the essential spectrum. Our goal is to develop an "axiomatic approach," which frees the linear theory from any nonlinear context in which it may have arisen.[PUBLICATION ABSTRACT]
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title Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: II
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