Application of the Wavelet Transform with a Piecewise Linear Basis to the Evaluation of the Hankel Transform

摘要

A method for computing the Hankel transform is proposed whereby the letter isreduced to a sum by representing the integrand as a smooth function times aBessel function. The smooth function is replaced by its wavelet decompositionwith a basis such that its scalar product with the Bessel function iscalculated analytically. The result is represented as a series, with thecoefficients strongly depending on the local behavior of the function beingtransformed. The application of the method is demonstrated by an exampleillustrated with plots.