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July 2016 A probabilistic approach to the zero-mass limit problem for three magnetic relativistic Schrödinger heat semigroups
Taro Murayama
Tsukuba J. Math. 40(1): 1-28 (July 2016). DOI: 10.21099/tkbjm/1474747485

Abstract

We consider three magnetic relativistic Schrödinger operators which correspond to the same classical symbol $\sqrt{(\xi - A(x))^2 + m^2} + V(x)$ and whose heat semigroups admit the Feynman-Kac-Itô type path integral representation $E[e^{ - S^m (x,\,t;\,X)} g(x + X(t))]$. Using these representations, we prove the convergence of these heat semigroups when the mass-parameter $m$ goes to zero. Its proof reduces to the convergence of $e^{- S^m (x,\,t;\,X)}$, which yields a limit theorem for exponentials of semimartingales as functionals of Lévy processes $X$.

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Taro Murayama. "A probabilistic approach to the zero-mass limit problem for three magnetic relativistic Schrödinger heat semigroups." Tsukuba J. Math. 40 (1) 1 - 28, July 2016. https://doi.org/10.21099/tkbjm/1474747485

Information

Received: 27 March 2015; Revised: 15 March 2016; Published: July 2016
First available in Project Euclid: 24 September 2016

zbMATH: 1350.60066
MathSciNet: MR3550930
Digital Object Identifier: 10.21099/tkbjm/1474747485

Subjects:
Primary: 35S10, 60F17, 60G51, 60H05, 81S40

Rights: Copyright © 2016 University of Tsukuba, Institute of Mathematics

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Vol.40 • No. 1 • July 2016
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