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Spectral properties of Schrödinger operators and time-decay of the wave functions. Results in \(L^ 2(R^ 4)\). (English) Zbl 0564.35024

The author considers Schrödinger operators \(H=-\Delta +V\) in \(L^ 2({\mathbb{R}}^ 4)\), where \(V(x)=O(| x|^{-\beta})\) as \(| x| \to \infty\) for some \(\beta >0\). Furthermore some local singularities are permitted. He is concerned with the spectral properties of H in the low energy limit. The results are expressed in terms of asymptotic expansions for the resolvent \(R(\zeta)=(H-\zeta)^{-1}\) as \(\zeta\) \(\to 0\).
Reviewer: N.Jacob

MSC:

35J10 Schrödinger operator, Schrödinger equation
35Q99 Partial differential equations of mathematical physics and other areas of application
35P05 General topics in linear spectral theory for PDEs
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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