Mellin analysis and its basic associated metric -- applications to sampling theory

DOI10.1007/s10476-016-0401-9zbMath1374.44001arXiv1603.04202OpenAlexW2559953642MaRDI QIDQ520060

Paul L. Butzer, Gerhard Schmeisser, Ilaria Mantellini, Carlo Bardaro

Publication date: 31 March 2017

Published in: Analysis Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.04202

zbMATH Keywords

Mellin transformapproximate reproducing kernel formulaapproximate sampling formulaMellin band-limited functionsMellin derivativeMellin distanceMellin-Bernstein inequalityMellin-Bernstein spaceMellin-Sobolev spaces

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Inequalities involving derivatives and differential and integral operators (26D10) General integral transforms (44A05)

Related Items (11)

Quadrature formulae for the positive real axis in the setting of Mellin analysis: sharp error estimates in terms of the Mellin distance ⋮ Some applications of modular convergence in vector lattice setting ⋮ A generalization of the Paley-Wiener theorem for Mellin transforms and metric characterization of function spaces ⋮ A retrospective on research visits of Paul Butzer's Aachen research group to Eastern Europe and Tenerife ⋮ Mellin integral transforms and generalized Lipschitz and Zygmund spaces ⋮ Jackson's inequalities in Mellin's analysis ⋮ Mellin transform of log-Lipschitz functions and equivalence of \(K\)-functionals and modulus of smoothness generated by the Mellin Steklov operator ⋮ To multidimensional Mellin analysis: Besov spaces, \(K\)-functor, approximations, frames ⋮ Exponential sampling series: convergence in Mellin-Lebesgue spaces ⋮ A retrospective on research visits of Paul Butzer's Aachen research group to North America and Western Europe ⋮ Some new estimates concerning the Mellin transform on the space \(X_c^2\)

Cites Work

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• Mellin transform analysis and integration by parts for Hadamard-type fractional integrals
• The foundations of fractional calculus in the Mellin transform setting with applications
• Numerical differentiation inspired by a formula of R.P. Boas
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• A self-contained approach to mellin transform analysis for square integrable functions; applications
• Exponential-sampling method for Laplace and other dilationally invariant transforms: I. Singular-system analysis
• The Derivative of a Trigonometric Integral

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