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ArticleOriginal scientific text

Title

Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains

Authors 1, 1

Affiliations

  1. Institute of Mathematics, Technical University of Wrocław, 50-370 Wrocław, Poland

Abstract

The purpose of the paper is to extend results of the potential theory of the classical Schrödinger operator to the α-stable case. To obtain this we analyze a weak version of the Schrödinger operator based on the fractional Laplacian and we prove the Conditional Gauge Theorem.

Keywords

ENG
α-stable Lévy processes, α-stable Feynman-Kac semigroup, weak fractional Laplacian, α-stable Schrödinger operator, potential theory, q-harmonic functions, conditional gauge theorem

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Studia Mathematica
1999/133/1
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Pages:
53-92
Main language of publication
English
Received
1998-03-23
Accepted
1998-06-29
Published
1999
Exact and natural sciences