On approximation by dilations of distributions

Sav Roman Harasymiv

Vol. 28 (1969), No. 2, 363–374

DOI: 10.2140/pjm.1969.28.363

Abstract

Let E be a locally convex space of temperate distributions and suppose that u ∈ E. We attempt to characterize the closed vector subspace of E generated by the set of all distributions having the form u(a₁x₁ + b₁,⋯,a_tx_n + b_n) where a₁,⋯,a_n, b₁,⋯,b_n are real numbers with a₁,⋯,a_n being nonzero. The characterization is effected in the case when the topology on E satisfies certain conditions.

Mathematical Subject Classification

Primary: 46.40

Milestones

Received: 9 August 1967

Published: 1 February 1969