Multi-variate Hardy-type lattice point summation and Shannon-type sampling

DOI10.1007/s13137-015-0076-6zbMath1369.94143OpenAlexW2160128318MaRDI QIDQ901330

M. Zuhair Nashed, Willi Freeden

Publication date: 11 January 2016

Published in: GEM - International Journal on Geomathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13137-015-0076-6

zbMATH Keywords

Gaussian summability of cardinal seriesHardy-type lattice point summationShannon-type sampling

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) General harmonic expansions, frames (42C15) Sampling theory in information and communication theory (94A20)

Related Items (1)

Gauss as Scientific Mediator Between Mathematics and Geodesy from the Past to the Present

Cites Work

• 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
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Special functions of mathematical (geo-)physics
• The Euler-MacLaurin summation formula, the sampling theorem, and approximate integration over the real axis
• General sampling theorems for functions in reproducing kernel Hilbert spaces
• Convolution, average sampling, and a Calderon resolution of the identity for shift-invariant spaces
• Average sampling in \(L^2\)
• Frames in spaces with finite rate of innovation
• Hermite interpolation and its numerical differentiation formula involving symmetric functions
• The sampling theorem and linear prediction in signal analysis
• Geometric and analytic number theory. Transl. from the German by Rudolf Taschner
• Approximations via Whittaker's cardinal function
• Eine Verallgemeinerung der Hardy-Landauschen Identität
• Advanced topics in Shannon sampling and interpolation theory
• Analysis of spherical symmetries in Euclidean spaces
• Sampling expansions and interpolation in unitarily translation invariant reproducing kernel Hilbert spaces
• Sampling of bandlimited functions on unions of shifted lattices
• Interpolation by multidimensional periodic splines
• Nonuniform average sampling and reconstruction in multiply generated shift-invariant spaces
• Sampling and reconstruction of signals in a reproducing kernel subspace of \(L^p(\mathbb R^d)\)
• Local reconstruction for sampling in shift-invariant spaces
• New perspectives on approximation and sampling theory. Festschrift in honor of Paul Butzer's 85th birthday
• An introduction to the geometry of numbers.
• Über die ganzen Lösungen der Wellengleichung
• Eine Erweiterung der Hardyschen Identität
• Grundbegriffe der Geometrie der Zahlen
• Eine Formel der analytischen Zahlentheorie
• Eine Verallgemeinerung der Eulerschen Summenformel und ihre Anwendung auf Fragen der analytischen Zahlentheorie
• Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces
• Approximation by Nonlinear Multivariate Sampling Kantorovich Type Operators and Applications to Image Processing
• Multiscale Signal Analysis and Modeling
• Sampling Expansions in Reproducing Kernel Hilbert and Banach Spaces
• Nonuniform Average Sampling and Reconstruction of Signals with Finite Rate of Innovation
• Five short stories about the cardinal series
• The Shannon sampling theorem—Its various extensions and applications: A tutorial review
• Numerical Methods Based on Whittaker Cardinal, or Sinc Functions
• A sampling theorem for wavelet subspaces
• Sampling Theory for not Necessarily Band-Limited Functions: A Historical Overview
• Generalized sampling expansion
• Sampling-50 years after Shannon
• Inverse Problems, Image Analysis, and Medical Imaging
• Shannon sampling and function reconstruction from point values
• Mathematical Analysis, Wavelets, and Signal Processing
• Function Spaces for Sampling Expansions
• Sampling signals with finite rate of innovation
• Frames and Operator Theory in Analysis and Signal Processing
• A Generalized Sampling Theorem
• Applications of reproducing kernel Hilbert spaces–bandlimited signal models
• On the geometry of numbers
• \(p\)-frames and shift invariant subspaces of \(L^p\)
• Modern sampling theory. Mathematics and applications

This page was built for publication: Multi-variate Hardy-type lattice point summation and Shannon-type sampling