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Non‐local Dirichlet forms generated by pseudodifferential operators on compact abelian groups
Author(s) -
Popescu Emil
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700692
Subject(s) - abelian group , mathematics , countable set , pure mathematics , domain (mathematical analysis) , dirichlet distribution , extension (predicate logic) , function (biology) , combinatorics , mathematical analysis , computer science , boundary value problem , evolutionary biology , biology , programming language
Let G i , 1 ≤ i ≤ n , be compact abelian groups and let Γ i , 1 ≤ i ≤ n , be countable dual groups. We consider G = G 1 ⊕ G 2 ⊕ … ⊕ G n and Γ = Γ 1 ⊕ Γ 2 ⊕ … ⊕ Γ n . For 1 ≤ j ≤ n , let a j be a negative definite function on Γ j and a ( γ ) = . For φ ∈ S ( G ), the set of all generalized trigonometrical polynomials on G , we define , where ( γ ) = a j ( γ j ) ( γ ), 1 ≤ j ≤ n . Then is a Dirichlet form with the domain on L 2 ( G ). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)