Open Access
Translator Disclaimer
July, 2010 Lp-independence of spectral bounds of Schrödinger-type operators with non-local potentials
Yoshihiro TAWARA
J. Math. Soc. Japan 62(3): 767-788 (July, 2010). DOI: 10.2969/jmsj/06230767


We establish a necessary and sufficient condition for spectral bounds of a non-local Feynman-Kac semigroup being Lp-independent. This result is an extension of that in [24] to more general symmetric Markov processes; in [24], we only treated a symmetric stable process on Rd. For example, we consider a symmetric stable process on the hyperbolic space, the jump process generated by the fractional power of the Laplace-Beltrami operator, and prove that by adding a non-local potential, the associated Feynman-Kac semigroup satisfies the Lp-independence.


Download Citation

Yoshihiro TAWARA. "Lp-independence of spectral bounds of Schrödinger-type operators with non-local potentials." J. Math. Soc. Japan 62 (3) 767 - 788, July, 2010.


Published: July, 2010
First available in Project Euclid: 30 July 2010

zbMATH: 1205.60138
MathSciNet: MR2648062
Digital Object Identifier: 10.2969/jmsj/06230767

Primary: 60J25
Secondary: 60J75

Keywords: Dirichlet form , Feynman-Kac formula , Lp-independence , Markov process

Rights: Copyright © 2010 Mathematical Society of Japan


Vol.62 • No. 3 • July, 2010
Back to Top