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1-Forms and Polar Decomposition on Harmonic Spaces

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Abstract

The article introduces substitutes for differential 1-forms on self-adjoint harmonic spaces by means of tensor products and energy norms. A representation using indicators of open sets connects 1-forms and topology. Finally, an orthogonal decomposition into exact and harmonic forms is provided, along with a description of harmonic forms in terms of locally harmonic functions.

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  1. Mathematisches Institut, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, 07737, Jena, Germany

    Michael Hinz

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  1. Michael Hinz
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Hinz, M. 1-Forms and Polar Decomposition on Harmonic Spaces. Potential Anal 38, 261–279 (2013). https://doi.org/10.1007/s11118-012-9272-2

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