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Estimate of the difference between the Kac operator and the Schrödinger semigroup

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Abstract

An operator norm estimate of the difference between the Kac operator and the Schrödinger semigroup is proved and used to give a variant of the Trotter product formula for Schrödinger operators in theL p operator norm. This extends Helffer’s result in theL 2 operator norm to the case in theL p operator norm for more general scalar potentials and with vector potentials. The method of the proof is probabilistic based on the Feynman—Kac and Feynman—Kac—Itô formula.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Kanazawa University, 920-11, Kanazawa, Japan

    Takashi Ichinose & Satoshi Takanobu

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  1. Takashi Ichinose
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  2. Satoshi Takanobu
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Research partially supported by Grant-in-Aid for Scientific Research No. 07454023, Ministry of Education, Science and Culture, Japanese Government.

Research partially supported by Grant-in-Aid for Scientific Research No. 07640293, Ministry of Education, Science and Culture, Japanese Government.

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Ichinose, T., Takanobu, S. Estimate of the difference between the Kac operator and the Schrödinger semigroup. Commun. Math. Phys. 186, 167–197 (1997). https://doi.org/10.1007/BF02885677

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  • DOI: https://doi.org/10.1007/BF02885677

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