A family of Riesz distributions for differential forms on Euclidian space

Fischmann Matthias; Ørsted Bent

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arXiv · 1702.00930

A family of Riesz distributions for differential forms on Euclidian space

Fischmann Matthias·Ørsted Bent

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Abstract

In this paper we introduce a new family of operator-valued distributions on Euclidian space acting by convolution on differential forms. It provides a natural generalization of the important Riesz distributions acting on functions, where the corresponding operators are $(-\Delta)^{-\alpha/2}$, and we develop basic analogous properties with respect to meromorphic continuation, residues, Fourier transforms, and relations to conformal geometry and representations of the conformal group.

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Fischmann Matthias, Ørsted Bent. 2017-02-03. A family of Riesz distributions for differential forms on Euclidian space. https://arxiv.org/abs/1702.00930

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