## Journal of the Mathematical Society of Japan

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

Yoshihiro TAWARA

#### Abstract

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

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

Dates
First available in Project Euclid: 30 July 2010

https://projecteuclid.org/euclid.jmsj/1280496819

Digital Object Identifier
doi:10.2969/jmsj/06230767

Mathematical Reviews number (MathSciNet)
MR2648062

Zentralblatt MATH identifier
1205.60138

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

#### Citation

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. https://projecteuclid.org/euclid.jmsj/1280496819

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