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Spectral Shift Function for Trapping Energies¶in the Semiclassical Limit

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Abstract:

Semiclassical asymptotics of the spectral shift function (SSF) for Schrödinger operator is studied at trapping energies. It is shown that the SSF converges to sum of a smooth function and a step function, which is essentially the counting function of resonances. In particular, the Weyl asymptotics is proved.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1, Komaba, Meguro-ku,¶Tokyo 153-8914, Japan. E-mail: shu@ms.u-tokyo.ac.jp, , , , , , JP

    Shu Nakamura

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  1. Shu Nakamura
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Received: 14 December 1998 / Accepted: 1 June 1999

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Nakamura, S. Spectral Shift Function for Trapping Energies¶in the Semiclassical Limit. Comm Math Phys 208, 173–193 (1999). https://doi.org/10.1007/s002200050753

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  • DOI: https://doi.org/10.1007/s002200050753

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