Journal of the Mathematical Society of Japan

Lp-independence of spectral bounds of Schrödinger-type operators with non-local potentials

Yoshihiro TAWARA

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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.

Article information

J. Math. Soc. Japan, Volume 62, Number 3 (2010), 767-788.

First available in Project Euclid: 30 July 2010

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Zentralblatt MATH identifier

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60J75: Jump processes

Feynman-Kac formula Lp-independence Dirichlet form Markov process


TAWARA, Yoshihiro. L p -independence of spectral bounds of Schrödinger-type operators with non-local potentials. J. Math. Soc. Japan 62 (2010), no. 3, 767--788. doi:10.2969/jmsj/06230767.

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