In this paper, we prove a representation theorem for the usual distributional Fourier transform over the spaces \(\mathscr{P}_{k}^{\prime}, k \in \mathbb{Z}, k<0\). An inversion formula is also obtained, which enables us to prove that \(\mathscr{Y}_{k}^{\prime}\) is a commutative convolution algebra
On the Fourier Transform in the Space L2(−∞, +∞)
✍ Scribed by Ashot Vagharshakyan
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 152 KB
- Volume
- 168
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
In this paper we give new representations for the Fourier transform and we establish the relation between those representations and the well known uncertainty principle.
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