A generalization of the Paley-Wiener theorem for Mellin transforms and metric characterization of function spaces

DOI10.1515/FCA-2017-0064zbMath1377.44004OpenAlexW2767540936MaRDI QIDQ1677975

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

Publication date: 14 November 2017

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/fca-2017-0064

zbMATH Keywords

Mellin transformsPaley-Wiener spacespolar-analytic functionsfractional Mellin derivativesfractional Mellin-Sobolev spacesMellin-Hardy spaces

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Fractional derivatives and integrals (26A33)

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 ⋮ Polar-analytic functions: old and new results, applications ⋮ 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 ⋮ On the existence of solutions to an inhomogeneous pantograph type equation with singular coefficients ⋮ Development of a new concept of polar analytic functions useful in Mellin analysis ⋮ 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 \(X_c^2\)

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