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

Abstract

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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.

How to cite

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Bogdan, 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 -

References

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