Analytic Properties of Fractional Schrödinger Semigroups and Gibbs Measures for Symmetric Stable Processes
نویسنده
چکیده
We establish a Feynman-Kac-type formula to define fractional Schrödinger operators for (fractional) Kato-class potentials as self-adjoint operators. In this functional integral representation symmetric α-stable processes appear instead of Brownian motion. We derive asymptotic decay estimates on the ground state for potentials growing at infinity. We prove intrinsic ultracontractivity of the Feynman-Kac semigroup, introduce the concept of asymptotic intrinsic ultracontractivity, and discuss their relationship and the borderline case of potentials. Finally, we construct Gibbs measures for symmetric stable processes, and prove their uniqueness and support properties.
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