CHARACTERIZATIONS of the INVERSION FORMULA of the CONTINUOUS BESSEL WAVELET TRANSFORM of DISTRIBUTIONS in H μ ′ (ℝ+)

Abstract

The inversion formula of the continuous Bessel wavelet transform of distributions is investigated by exploiting the theory of the Hankel transform. Some auxiliary results related to the inversion formula are also obtained in this paper. Using the theory of inversion formula of continuous Bessel wavelet transform of distributions, the Calderón reproducing formula is developed. The continuous Bessel wavelet transform of distributions through heat equation is discussed and its inversion formula is considered. © 2023 The Author(s).