Quadrature formulae for the positive real axis in the setting of Mellin\n analysis: Sharp error estimates in terms of the Mellin distance

2018/02/12 by Carlo Bardaro, P. L. Butzer, Bardaro, Carlo +5
Computer Science · Mathematics · #26A33 #41A80 #65D30 #65D32 #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1802.03952

openalex publication_date 2018/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The general Poisson summation formula of Mellin analysis can be considered as\na quadrature formula for the positive real axis with remainder. For Mellin\nbandlimited functions it becomes an exact quadrature formula. Our main aim is\nto study the speed of convergence to zero of the remainder for a function f\nin terms of its distance from a space of Mellin bandlimited functions. The\nresulting estimates turn out to be of best possible order. Moreover, we\ncharacterize certain rates of convergence in terms of Mellin--Sobolev and\nMellin--Hardy type spaces that contain f. Some numerical experiments\nillustrate and confirm these results.\n

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