Abstract
In this paper we extend the classical theory of the Fourier transofrm on the space of tempered distributions. We construct a testing function space which is contained and dense in the space of rapidly decreasing functions. We introduce and study the properties of the Fourier transform on this testing function space as a prelude to the introduction of the Fourier transform on its dual. We also obtain an inversion theorem for this Fourier transform. These investigations enable us to obtain a representation theorem for the elements of the dual of this space.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 133-148 |
| Number of pages | 16 |
| Journal | Integral Transforms and Special Functions |
| Volume | 9 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2000 |
| Externally published | Yes |
Bibliographical note
Funding Information:Research of the second author is supported by a senior research fellowship from CSIR, India. We thank Professor Kenneth B. Howell and a referee for their valuable comments.
Keywords
- Convolution
- Fourier transform
- Rapidly decreasing functions
- Representation theorems
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