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Asymptotic and analytic properties of resonance functions. (English) Zbl 0713.35067

We discuss resonances of Schrödinger operators \(H=-\Delta +V+W\), where V is a dilation-analytic, short-range and W exponentially decaying potential. Resonances are defined as poles of the analytically continued resolvent of H and identified with poles of the analytically continued resolvent of H and identified with poles of the analytically extended S- matrix. Resonance functions associated with a resonance \(k_ 0\) are defined as certain exponentially growing solutions u of the Schrödinger equation \((H-k^ 2_ 0)u=0\), and an isomorphism is established between the space of resonance functions and the null space of the analytically continued inverse S-matrix.
Reviewer: E.Balslev

MSC:

35P25 Scattering theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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References:

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