Exponential sampling series: convergence in Mellin-Lebesgue spaces
DOI10.1007/S00025-019-1044-5zbMath1461.41003OpenAlexW2947070380WikidataQ115609475 ScholiaQ115609475MaRDI QIDQ2311967
Ilaria Mantellini, Carlo Bardaro, Gerhard Schmeisser
Publication date: 4 July 2019
Published in: Results in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00025-019-1044-5
General harmonic expansions, frames (42C15) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Sampling theory in information and communication theory (94A20)
Related Items (22)
Cites Work
- On the Paley-Wiener theorem in the Mellin transform setting
- Asymptotic formulae for linear combinations of generalized sampling operators
- Shannon's sampling theorem for bandlimited signals and their Hilbert transform, Boas-type formulae for higher order derivatives -- the aliasing error involved by their extensions from bandlimited to non-bandlimited signals
- Basic relations valid for the Bernstein space \(B^{p}_{\sigma}\) and their extensions to functions from larger spaces with error estimates in terms of their distances from \(B^{p}_{\sigma}\)
- Mellin analysis and its basic associated metric -- applications to sampling theory
- Approximation error of the Whittaker cardinal series in terms of an averaged modulus of smoothness covering discontinuous signals
- Rate of approximation for nonlinear integral operators with application to signal processing
- Obtaining a function of bounded coarse variation by a change of variable
- The sampling theorem and linear prediction in signal analysis
- A direct approach to the Mellin transform
- Improper integrals, simple integrals, and numerical quadrature
- Inverse results of approximation and the saturation order for the sampling Kantorovich series
- Approximation of discontinuous signals by sampling Kantorovich series
- The Mellin–Parseval formula and its interconnections with the exponential sampling theorem of optical physics
- The sampling theorem, Poisson's summation formula, general Parseval formula, reproducing kernel formula and the Paley–Wiener theorem for bandlimited signals – their interconnections
- A general approximation result for nonlinear integral operators and applications to signal processing*
- Prediction of Non-Bandlimited Signals from Past Samples in Terms of Splines of Low Degree
- Approximation results for nonlinear integral operators in modular spaces and applications
- A self-contained approach to mellin transform analysis for square integrable functions; applications
- A generalization of the exponential sampling series and its approximation properties
- A fresh approach to the Paley–Wiener theorem for Mellin transforms and the Mellin–Hardy spaces
- A characterization of the convergence in variation for the generalized sampling series
- Prediction by Samples From the Past With Error Estimates Covering Discontinuous Signals
- Seven pivotal theorems of Fourier analysis, signal analysis, numerical analysis and number theory: their interconnections
- Approximation properties in abstract modular spaces for a class of general sampling-type operators
- Exponential-sampling method for Laplace and other dilationally invariant transforms: II. Examples in photon correlation spectroscopy and Fraunhofer diffraction
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Exponential sampling series: convergence in Mellin-Lebesgue spaces