The Continuous Wavelet Transform for A Bessel Type Operator on the Half Line

Abstract

We consider a singular differential operator Δ on the half line which generalizes the Bessel operator. Using harmonic analysis tools corresponding to Δ, we construct and investigate a new continuous wavelet transform on [0,∞[ tied to Δ. We apply this wavelet transform to invert an intertwining operator between Δ and the second derivative operator d²/dx².