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The norm estimate of the difference between the Kac operator and the Schrödinger semigroup: A unified approach to the nonrelativistic and relativistic cases

Published online by Cambridge University Press:  22 January 2016

Takashi Ichinose  and
Satoshi Takanobu
Takashi Ichinose
Affiliation:
Department of Mathematics, Faculty of Science, Kanazawa University, Kanazawa, 920-1192, Japan, ichinose@kappa.s.kanazawa-u.ac.jp
Satoshi Takanobu
Affiliation:
Department of Mathematics, Faculty of Science, Kanazawa University, Kanazawa, 920-1192, Japan, takanobu@kappa.s.kanazawa-u.ac.jp
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Abstract.

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An Lp 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 the Lp operator norm. The method of the proof is probabilistic based on the Feynman-Kac formula. The problem is discussed in the relativistic as well as nonrelativistic case.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 149 , March 1998 , pp. 53 - 81
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

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