Potential theory of Schrödinger operator based on fractional Laplacian

• Autorzy: Bogdan K. , Byczkowski T.
• Języki publikacji: EN

Abstrakty

EN

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 R^d, 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.

Słowa kluczowe

EN

symmetric α-stable Lévy process; Feynman-Kac semigroup; Schrödinger operators; q-harmonic function; Kelvin transform; conditional gauge theorem

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2000
• Tom: Vol. 20, Fasc. 2
• Strony: 293--335
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Bogdan K.

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Byczkowski T.

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

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