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Schrödinger operators with complex-valued potentials and no resonances | | T. Christiansen
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26 Aug 2004 | | Subject: | Mathematical Physics; Spectral Theory MSC-class: 35P25; 47A40; 81U05; 58J50 | math-ph math.MP math.SP | | Abstract: | In dimension $dgeq 3$, we give examples of nontrivial, compactly supported, complex-valued potentials such that the associated Schrödinger operators have no resonances. If $d=2$, we show that there are potentials with no resonances away from the origin. These Schrödinger operators are isophasal and have the same scattering phase as the Laplacian on $Real^d$. In odd dimensions $dgeq 3$ we study the fundamental solution of the wave equation perturbed by such a potential. If the space variables are held fixed, it is super-exponentially decaying in time. | | Source: | arXiv, math-ph/0408052 | | Services: | Forum | Review | PDF | Favorites | |
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