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

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

2004-06-14

arxiv.org/abs/math/0406263v1

Comp. Math. and Math. Phys., Vol. 44, No. 3, 2004, pp. 396-400

Mathematics

Numerical Analysis

Scientific paper

A method for computing the Hankel transform is proposed whereby the letter is reduced to a sum by representing the integrand as a smooth function times a Bessel function. The smooth function is replaced by its wavelet decomposition with a basis such that its scalar product with the Bessel function is calculated analytically. The result is represented as a series, with the coefficients strongly depending on the local behavior of the function being transformed. The application of the method is demonstrated by an example illustrated with plots.

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