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Dirichlet forms on symmetric spaces

Christian Berg — 1973

Annales de l'institut Fourier

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 compact type...

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