Vol. 31, No. 2, 1969

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Dilations of rapidly decreasing functions

Sav Roman Harasymiv

Vol. 31 (1969), No. 2, 395–402
Abstract

Let S be the space of rapidly decreasing indefinitely differentiable functions on the n-dimensional Euclidean space Rn, and suppose that ϕ S. We attempt to characterize the closed vector subspace of S which is generated by the set of all functions of the form

(x1,⋅⋅⋅ ,xn) → ϕ(a1x1 + b1,⋅⋅⋅ ,aniljn + bn)

where a1,,an,b1,,bn are real numbers, with a1,,an nonzero. We also consider an analogous approximation problem in the space Sof temperate distribution on Rn.

Mathematical Subject Classification
Primary: 46.40
Milestones
Received: 16 February 1968
Published: 1 November 1969
Authors
Sav Roman Harasymiv