On the representation of Dirichlet forms

Lars-Erik Andersson

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Dirichlet forms on symmetric spaces

Christian Berg (1973)

Annales de l'institut Fourier

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Let $G$ be a locally compact group and $K$ a compact subgroup such that the algebra $L^{1} (G)^{♯}$ of biinvariant integrable functions is commutative. We characterize the $G$ -invariant Dirichlet forms on the homogeneous space $G / K$ using harmonic analysis of $L^{1} (G)^{♯}$ . This extends results from Ch. Berg, Séminaire Brelot-Choquet-Deny, Paris, 13e année 1969/70 and J. Deny, Potential theory (C.I.M.E., I ciclo, Stresa), Ed. Cremonese, Rome, 1970. Every non-zero $G$ -invariant Dirichlet form on a symmetric space $G / K$ of non...