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

Krzysztof Bogdan; Tomasz Byczkowski

Studia Mathematica (1999)

- Volume: 133, Issue: 1, page 53-92
- ISSN: 0039-3223

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topBogdan, Krzysztof, and Byczkowski, Tomasz. "Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains." Studia Mathematica 133.1 (1999): 53-92. <http://eudml.org/doc/216605>.

@article{Bogdan1999,

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.},

author = {Bogdan, Krzysztof, Byczkowski, Tomasz},

journal = {Studia Mathematica},

keywords = {α-stable Lévy processes; α-stable Feynman-Kac semigroup; weak fractional Laplacian; α-stable Schrödinger operator; potential theory; q-harmonic functions; conditional gauge theorem; -stable Lévy processes; -stable Feyman-Kac semi-group; -stable Schrödinger operator; -harmonic functions},

language = {eng},

number = {1},

pages = {53-92},

title = {Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains},

url = {http://eudml.org/doc/216605},

volume = {133},

year = {1999},

}

TY - JOUR

AU - Bogdan, Krzysztof

AU - Byczkowski, Tomasz

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

JO - Studia Mathematica

PY - 1999

VL - 133

IS - 1

SP - 53

EP - 92

AB - 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.

LA - eng

KW - α-stable Lévy processes; α-stable Feynman-Kac semigroup; weak fractional Laplacian; α-stable Schrödinger operator; potential theory; q-harmonic functions; conditional gauge theorem; -stable Lévy processes; -stable Feyman-Kac semi-group; -stable Schrödinger operator; -harmonic functions

UR - http://eudml.org/doc/216605

ER -

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