Vol. 55, No. 2, 1974

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Groups of matrices acting on distribution spaces

Sav Roman Harasymiv

Vol. 55 (1974), No. 2, 403–417

Let E be a locally convex space of temperate distributions on the n-dimensional Euclidean space Rn, and G a closed subgroup of Gl(n,R), the general linear group over Rn. An attempt is made to identify those distributions which can be approximated in E by linear combinations of distributions of the form u(Ax + b), where u is a fixed element of E, A varies over G, and b varies over Rn. A cancellation theorem is proved; this then allows the support of the Fourier transform of any annihilator of the set of distributions of the form u(Ax + b) to be localized. This in turn is used to obtain approximation results.

Mathematical Subject Classification 2000
Primary: 46F10
Received: 6 June 1973
Revised: 24 January 1974
Published: 1 December 1974
Sav Roman Harasymiv