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1 June 2006 Schrödinger operators with complex-valued potentials and no resonances
T. Christiansen
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Duke Math. J. 133(2): 313-323 (1 June 2006). DOI: 10.1215/S0012-7094-06-13324-0

Abstract

In dimension d3, we give examples of nontrivial, compactly supported, complex-valued potentials such that the associated Schrödinger operators have neither resonances nor eigenvalues. If d=2, we show that there are potentials with no resonances or eigenvalues away from the origin. These Schrödinger operators are isophasal and have the same scattering phase as the Laplacian on Rd. In odd dimensions d3, we study the fundamental solution of the wave equation perturbed by such a potential. If the space variables are held fixed, it is superexponentially decaying in time

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T. Christiansen. "Schrödinger operators with complex-valued potentials and no resonances." Duke Math. J. 133 (2) 313 - 323, 1 June 2006. https://doi.org/10.1215/S0012-7094-06-13324-0

Information

Published: 1 June 2006
First available in Project Euclid: 21 May 2006

zbMATH: 0476.03047
MathSciNet: MR2225694
Digital Object Identifier: 10.1215/S0012-7094-06-13324-0

Subjects:
Primary: 35P25
Secondary: 47A40, 81U05

Rights: Copyright © 2006 Duke University Press

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Vol.133 • No. 2 • 1 June 2006
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