Quaternionic fractional wavelet transform. (English) Zbl 1402.42008
Summary: The novel fractional wavelet transform is extended to the space of square integrable quaternion valued functions on \(\mathbb {R}\) and its properties like linearity, Parseval’s identity and inversion formula are derived.
MSC:
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 46S10 | Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis |
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
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