## Tempered Boehmians and ultradistributions.(English)Zbl 0821.46053

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
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