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An improved Combes-Thomas estimate of magnetic Schrödinger operators. (English) Zbl 1308.35283

Summary: In the present paper, we prove an improved Combes-Thomas estimate, viz. the Combes-Thomas estimate in trace-class norms, for magnetic Schrödinger operators under general assumptions. In particular, we allow for unbounded potentials. We also show that for any function in the Schwartz space on the reals the operator kernel decays, in trace-class norms, faster than any polynomial.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35Q60 PDEs in connection with optics and electromagnetic theory
35B45 A priori estimates in context of PDEs
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