We announce new results in the potential theory of Schroedinger operators based on the fractional Laplacian on Euclidean spaces of arbitrary dimension. We concentrate on questions related to gaugeability and existence of q-harmonic functions. Results are obtained by analyzing properties of symmetric [alpha]-stable Levy processes on Rd, including the recurrent case. We also provide some explicit examples of gauge functions for a general class of domains.
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We develop potential theory of Schrödinger operators based on fractional Laplacian on Euclidean spaces of arbitrary dimension. We focus on questions related to gaugeability and existence of q-harmonic functions. Results are obtained by analyzing properties of a symmetric α-stable Lévy process on Rd, including the recurrent case. We provide some relevant techniques and apply them to give explicit examples of gauge functions for a general class of domains.
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