A Bessel type operator and the continuous wavelet transform on the half line

Abstract

In this paper we consider a singular differential operator Ba,b,n on the half line which
generalizes the Bessel operator. We construct and investigate a new continuous wavelet transform on [0, ∞] tied to Ba,b,n by using harmonic analysis tools corresponding to

Ba,b,n. Further we this wavelet transform to invert an intervening operator between Ba,b,n and the second derivative operator Dx = d2/
dx2 .
Keywords: Singular differential operator, generalized wavelets, generalized continuous wavelet transform.
Mathematics subject classiï¬cation: 42A38, 43A15.