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Harmonic spaces associated with non-symmetric translation invariant Dirichlet forms

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Summary

Continuing earlier work on construction of harmonic spaces from translation invariant Dirichlet spaces defined on locally compact abelian groups, it is shown that the potential kernel for a non-symmetric translation invariant Dirichlet form on a locally compact abelian group under the extra assumptions that

  1. (i)

    the potential kernel is absolutely continuous and the “canonical” l.s.c. density is continuous in the complement of the neutral element.

  2. (ii)

    the theory is of local type.

  3. (iii)

    the underlying group is not discrete, can be interpreted as the potential kernel for a translation invariant axiomatic theory of harmonic functions, in which (among other properties) the domination axiom is fulfilled.

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References

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Authors and Affiliations

  1. Matematisk Institut, Universitetsparken 5, DK-2100, København Ø, Denmark

    G. Forst

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  1. G. Forst
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Forst, G. Harmonic spaces associated with non-symmetric translation invariant Dirichlet forms. Invent Math 34, 135–150 (1976). https://doi.org/10.1007/BF01425480

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  • DOI: https://doi.org/10.1007/BF01425480

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