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Riesz distributions. (English) Zbl 0773.46016
We study some properties of the Riesz distributions associated to a quadratic form of signature $$(m,n)$$. Although there is an extensive literature on this subject, the extent to which the Riesz distributions determine the space of all invariant distributions does not appear to have received the attention it deserves. This note is addressed to this issue. For clarity of exposition we have written this article in two parts: Section 1 deals with the hyperbolic case (of $$m=1$$), while Section 2 takes up the general case (including the situation of $$m=0$$).
This note is closely related to the longer part by the authors on Lorentz invariant distributions supported on the forward light cone associated with a form of signature $$(1,n)$$ [to appear in Composito Math.].

##### MSC:
 46F05 Topological linear spaces of test functions, distributions and ultradistributions
##### Keywords:
Riesz distributions; quadratic form; hyperbolic case
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