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On the Spectrum of a Class of Non‐Sectorial Diffusion Operators
Author(s) -
Röckner Michael,
Wang FengYu
Publication year - 2004
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460930300273x
Subject(s) - mathematics , class (philosophy) , spectrum (functional analysis) , diffusion , pure mathematics , physics , computer science , quantum mechanics , artificial intelligence
In terms of the upper bounds of a second‐order elliptic operator acting on specific Lyapunov‐type functions with compact level sets, sufficient conditions are presented for the corresponding Dirichlet form to satisfy the Poincaré and the super‐Poincaré inequalities. Here, the elliptic operator is assumed to be symmetric on L 2 (μ) with some probability measure μ. As applications, proofs are given for a class of (non‐symmetric) diffusion operators generating C 0 ‐semigroups on L 1 (μ): that their L p (μ)‐essential spectrum is empty for p > 1. This follows since it is proved that their C 0 ‐semigroups are compact. 2000 Mathematics Subject Classification 47D07, 60H10.