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

M. Burak Erdoğan | Zendy; Wilhelm Schlag | Zendy

Open Access

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

Author(s) -

M. Burak Erdoğan,

Wilhelm Schlag

Publication year - 2006

Publication title -

journal d analyse mathématique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.189

H-Index - 53

eISSN - 1565-8538

pISSN - 0021-7670

DOI - 10.1007/bf02789446

Subject(s) - eigenvalues and eigenvectors , mathematics , dimension (graph theory) , context (archaeology) , zero (linguistics) , operator (biology) , essential spectrum , nonlinear system , spectral theory , spectrum (functional analysis) , mathematical physics , resonance (particle physics) , mathematical analysis , energy (signal processing) , physics , pure mathematics , quantum mechanics , philosophy , gene , paleontology , linguistics , biochemistry , chemistry , repressor , hilbert space , transcription factor , biology

We consider non-selfadjoint operators of the kind arising in linearized NLSand prove dispersive bounds for the time-evolution without assuming that theedges of the essential spectrum are regular. Our approach does not depend onany specific properties of NLS. Rather, it is axiomatic on the linear level,and our results are obtained from four assumptions (which are of coursemotivated by NLS). This work is in three dimensions.

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