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Contents of PMS, Vol. 20, Fasc. 2,
pages 293 - 335
 

POTENTIAL THEORY OF SCHRÖDINGER OPERATOR BASED ON FRACTIONAL LAPLACIAN

Krzysztof Bogdan
Tomasz Byczkowski

Abstract: 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 a -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.

1991 AMS Mathematics Subject Classification: Primary 31B2S, 60JS0.

Key words and phrases: symmetric a -stable Lévy process, Feynman-Kac semigroup, Schrödinger operator, q -harmonic functions, Kelvin transform, conditional gauge theorem.

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