Communications in Mathematical Physics

, Volume 186, Issue 1, pp 167–197

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

  • Takashi Ichinose
  • Satoshi Takanobu
Article

DOI: 10.1007/BF02885677

Cite this article as:
Ichinose, T. & Takanobu, S. Commun. Math. Phys. (1997) 186: 167. doi:10.1007/BF02885677

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 theLp operator norm. This extends Helffer’s result in theL2 operator norm to the case in theLp 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.

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Takashi Ichinose
    • 1
  • Satoshi Takanobu
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceKanazawa UniversityKanazawaJapan

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