Abstract
In this paper, we introduce the canonical Fourier transform associated with the Dunkl-type operator and study some of its important properties. We study the generalized translation operator and convolution product associated with this transform and present some of its basic properties. Next, at the heart of our investigation, we introduce and study the canonical wavelet transform associated with the generalized canonical Fourier transform. Nonetheless, special attention is paid to the applications of these new transforms.
| Original language | English |
|---|---|
| Pages (from-to) | 1-40 |
| Number of pages | 40 |
| Journal | Integral Transforms and Special Functions |
| DOIs | |
| Publication status | Published - 10 Jul 2025 |
Keywords
- Generalized canonical Fourier transform
- generalized canonical wavelet transform
- Dunkl-type operator
- Chébli–Trimèche hypergroup
- translation operator
- convolution product