The norm estimate of the difference between the Kac operator and Schrödinger semigroup. II: The general case including the relativistic case
type: Item
instance of: scholarly article
title: The norm estimate of the difference between the Kac operator and Schrödinger semigroup. II: The general case including the relativistic case
zbMATH Open document ID: 0987.47032
author: Satoshi Takanobu
author: Takashi Ichinose
published in: Electronic Journal of Probability
publication date: 2000-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/121856
full work available at URL: paper5.abs.html
review text: The authors' previous paper [Commun. Math. Phys. 186, No. 1, 167-197 (1997; Zbl 0912.47025) and Nagoya Math. J. 149, 53-81 (1998; Zbl 0917.47041)] discussed the \(L_p\)-operator norm estimate of difference between the Kac operator and the Schrödinger semigroup. In the present paper, more general Schrödinger operators associate with the Levy processes, including the reletivistic Schrödinger operators, are studied and the results are generalised. As an application, the Trotter product formula in the \(L_p\)-operator norm is derived. The method of proof is based on using the Feynman-Kac formula not directly for the operator, but instead through subordination from the Brownian motion to enable to deal with all operators in a unified way.
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J35
zbMATH DE Number: 1447300
zbMATH Keywords: Schrödinger semigroup
zbMATH Keywords: Schrödinger operators
zbMATH Keywords: Brownian motion
zbMATH Keywords: Trotter product formula
zbMATH Keywords: Lie-Trotter-Kato product formula
zbMATH Keywords: Feynman-Kac formula
zbMATH Keywords: subordination of Brownian motion
zbMATH Keywords: Kato's inequality
reviewed by: Minping Qian
MaRDI profile type: Publication
DOI: 10.1214/EJP.V5-61
description: scientific article; zbMATH DE number 1447300