The continuous fractional Bessel wavelet transform and its applications. (English) Zbl 07901560
Summary: In this paper, the fractional Bessel wavelet transform is introduced by exploiting the theory of the fractional Hankel transform and the boundedness of the fractional Bessel wavelet transform obtained. Time invariant linear filter associated with the fractional Hankel transform is investigated and its various properties are obtained. In the present paper, authors also expressed time-invariant linear filters in the form of the fractional Bessel wavelet transform and applications of the aforesaid filters in the integral equation are given.
MSC:
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 46F12 | Integral transforms in distribution spaces |
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
| 44A20 | Integral transforms of special functions |
Keywords:
fractional Hankel transform; continuous fractional Bessel wavelet transform; Parseval formula; fractional Hankel convolution; Caldron reproducing formula; time-invariant linear filtersReferences:
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