Tempered Boehmians and ultradistributions. (English) Zbl 0821.46053

Mikusiński, Piotr

Proc. Am. Math. Soc. 123, No. 3, 813-817 (1995).

Summary: An extension of the Fourier transform which is a one-to-one continuous mapping from the space of tempered Boehmians onto the space of Schwartz distributions is introduced. This shows that the space of tempered Boehmians can be identified with the space \({\mathcal Z}'\) of ultradistributions.

MSC:

46F12	Integral transforms in distribution spaces
44A40	Calculus of Mikusiński and other operational calculi
46F05	Topological linear spaces of test functions, distributions and ultradistributions
42B10	Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Keywords:

Fourier transform; one-to-one continuous mapping from the space of tempered Boehmians onto the space of Schwartz distributions; ultradistributions