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Lp-independence of spectral bounds of non-local Feynman-Kac semigroups

Masayoshi Takeda1 / Yoshihiro Tawara2

1Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan.

2Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan.

Citation Information: Forum Mathematicum. Volume 21, Issue 6, Pages 1067–1080, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/FORUM.2009.053, September 2009

Publication History

Received:
2007-05-29
Revised:
2008-03-31
Published Online:
2009-09-03

Abstract

For a symmetric stable process we consider a transform of its transition semigroup by a non-local Feynman-Kac functional. We prove that if the Feynman-Kac functional belongs to a certain class, then the spectral bound of the transformed semigroup on Lp (ℝd) is independent of p.

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