Sampling in reproducing kernel Banach spaces

DOI10.1007/s00009-012-0234-0zbMath1279.42035OpenAlexW1981495585MaRDI QIDQ358246

Antonio G. García, Alberto Portal

Publication date: 16 August 2013

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-012-0234-0

zbMATH Keywords

semi-inner productaverage samplingReproducing kernel Banach spacesShift-invariant spaces

Mathematics Subject Classification ID

Generalizations of inner products (semi-inner products, partial inner products, etc.) (46C50) General harmonic expansions, frames (42C15) Sampling theory in information and communication theory (94A20)

Related Items

A converse sampling theorem in reproducing kernel Banach spaces ⋮ On reproducing kernel Banach spaces: generic definitions and unified framework of constructions ⋮ Sparse Support Vector Machines in Reproducing Kernel Banach Spaces ⋮ Generalized Mercer Kernels and Reproducing Kernel Banach Spaces ⋮ Solutions of nonlinear systems by reproducing kernel method ⋮ The Kramer sampling theorem revisited ⋮ Seven pivotal theorems of Fourier analysis, signal analysis, numerical analysis and number theory: their interconnections ⋮ Sampling and Galerkin reconstruction in reproducing kernel spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regular multivariate sampling and approximation in \(L^p\) shift-invariant spaces
• Frames, Riesz bases, and sampling expansions in Banach spaces via semi-inner products
• General sampling theorems for functions in reproducing kernel Hilbert spaces
• Convolution, average sampling, and a Calderon resolution of the identity for shift-invariant spaces
• Representation of linear functionals in a Banach space
• Whittaker-Kotelnikov-Shannon sampling theorem and aliasing error
• On stability of sampling-reconstruction models
• Approximation from shift-invariant spaces by generalized sampling formulas
• Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces
• Semi-Inner-Product Spaces
• Sampling Expansions in Reproducing Kernel Hilbert and Banach Spaces
• Wiener’s Lemma: Theme and Variations. An Introduction to Spectral Invariance and Its Applications
• Sampling in the functional hilbert space induced by a hilbert space valued kernel
• Orthogonal Sampling Formulas: A Unified Approach
• On the localization and directionalization of uniform convexity
• Classes of Semi-Inner-Product Spaces
• Theory of Reproducing Kernels
• An introduction to frames and Riesz bases