L[p]-independence of spectral bounds of Schrodinger-type operators with non-local potentials

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  • <i>L<sup>p</sup></i>-independence of spectral bounds of Schrödinger-type operators with non-local potentials
  • Lp-independence of spectral bounds of Schrödinger-type operators with non-local potentials

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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.

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