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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 28, Fasc. 1,
pages 163 - 167
 

SPECTRAL GAP ESTIMATE FOR STABLE PROCESSES ON ARBITRARY BOUNDED OPEN SETS

Mateusz Kwaśnicki

Abstract: In the paper we prove the lower bound estimate $\lambda ^D_2 - \lambda ^D_1 \ge c (\lambda ^D_1)^(-(d)/(\alpha )) (\diam D)^(-d - \alpha )$ for the spectral gap of the Dirichlet fractional Laplacian $\gen $ on an arbitrary bounded open set $D \sub \Rd $.

2000 AMS Mathematics Subject Classification: Primary 47G30, 60G52.

Key words and phrases: Isotropic stable process, spectral gap.

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