General sampling theorems for functions in reproducing kernel Hilbert spaces

DOI10.1007/BF02570568zbMath0734.46019OpenAlexW2053159614MaRDI QIDQ810822

M. Zuhair Nashed, Gilbert G. Walter

Publication date: 1991

Published in: MCSS. Mathematics of Control, Signals, and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02570568

zbMATH Keywords

Sobolev spacetruncationHankel transformsjitterbandlimited signalsreproducing kernel Hilbert spacealiasingsampling theoremsnonuniform samplingamplitude errorJacobi transformsLguerre transformsorthogonal and nonorthogonal sampling sequencesprolate spherical transformssampling errorsSturm-Liouville transforms

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)

Related Items (45)

Optimal sampling points in reproducing kernel Hilbert spaces ⋮ The Zero-Removing Property and Lagrange-Type Interpolation Series ⋮ NEW BOUNDS FOR TRUNCATION-TYPE ERRORS ON REGULAR SAMPLING EXPANSIONS ⋮ Model Checks in Inverse Regression Models with Convolution-Type Operators ⋮ Sampling Theory and Reproducing Kernel Hilbert Spaces ⋮ On stability of sampling-reconstruction models ⋮ Sampling procedures in function spaces and asymptotic equivalence with shannon's sampling theory ⋮ A sampling theory for non-decaying signals ⋮ Families of multiresolution and wavelet spaces with optimal properties ⋮ Sampling in reproducing kernel Banach spaces ⋮ Functional reproducing kernel Hilbert spaces for non-point-evaluation functional data ⋮ Sampling analysis in the complex reproducing kernel Hilbert space ⋮ Multi-variate Hardy-type lattice point summation and Shannon-type sampling ⋮ Perturbed sampling formulas and local reconstruction in shift invariant spaces ⋮ Separability of reproducing kernel spaces ⋮ On a class of non-uniform average sampling expansions and partial reconstruction in subspaces of \(L _{2}(\mathbb R)\) ⋮ Spatiospectral concentration in the Cartesian plane ⋮ On the limit of sampled signal extrapolation with a wavelet signal model^∗ ⋮ Discrete orthogonality of the Malmquist Takenaka system of the upper half plane and rational interpolation ⋮ Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces ⋮ ON THE INCLUSION RELATION OF REPRODUCING KERNEL HILBERT SPACES ⋮ Inverse gravimetry: background material and multiscale mollifier approaches ⋮ Frames, Riesz bases, and sampling expansions in Banach spaces via semi-inner products ⋮ Sampling of bandlimited signals in fractional Fourier transform domain ⋮ A multi-level algorithm for the solution of moment problems ⋮ Sampling and reconstruction of signals in a reproducing kernel subspace of \(L^p(\mathbb R^d)\) ⋮ Wavelets based on orthogonal basic splines ⋮ Sampling and Galerkin reconstruction in reproducing kernel spaces ⋮ Time sampling and reconstruction in weighted reproducing kernel subspaces ⋮ Discrete Sampling Formulas on Spaces of p^M-Periodic Sequences for Computational Applications on Edge Detection ⋮ Sampling and Approximation in Shift Invariant Subspaces of $$L_2(\mathbb {R})$$ ⋮ Sampling of bandlimited signals in the offset linear canonical transform domain based on reproducing kernel Hilbert space ⋮ Approximation with impulse trains ⋮ Sampling in the functional hilbert space induced by a hilbert space valued kernel ⋮ Sampling Expansions in Reproducing Kernel Hilbert and Banach Spaces ⋮ Convolution sampling and reconstruction of signals in a reproducing kernel subspace ⋮ Gauss as Scientific Mediator Between Mathematics and Geodesy from the Past to the Present ⋮ Sampling and \(\Pi\)-sampling expansions ⋮ Exponential approximation of multivariate bandlimited functions from average oversampling ⋮ Approximating signals by fast impulse sampling ⋮ Finite lagrange and cauchy sampling expansions associated with regular difference equations^∗ ⋮ The zero-removing property in Hilbert spaces of entire functions arising in sampling theory ⋮ Uniqueness theorems for entire functions having growth [2, π/2) ⋮ On the duality of discrete and periodic functions ⋮ Hyper-Gaussian regularized Whittaker–Kotel’nikov–Shannon sampling series

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Laguerre transform of some elementary functions
• The sampling theorem and linear prediction in signal analysis
• The finite continuous Jacobi transform and its inverse
• Introduction to general theory of reproducing kernels
• Sampling Expansions for Functions Band-Limited in the Distributional Sense
• On Lagrange Interpolation and Kramer-Type Sampling Theorems Associated with Sturm–Liouville Problems
• Five short stories about the cardinal series
• The Shannon sampling theorem—Its various extensions and applications: A tutorial review
• Sampling expansion for a Languerre-La? transform
• Generalized Sampling Theorems for Bessel–Type Transforms of Bandlimited Functions and Distributions
• Convergence Rates of Approximate Least Squares Solutions of Linear Integral and Operator Equations of the First Kind
• Band-limited functions and the sampling theorem
• A Comparison of the Sampling Theorems of Kramer and Whittaker
• On the application of some interpolating functions in physics
• A Generalized Sampling Theorem
• Applications of reproducing kernel Hilbert spaces–bandlimited signal models
• Theory of Reproducing Kernels
• Eigenfunction Expansions Associated with Partial Differential Equations (II)

This page was built for publication: General sampling theorems for functions in reproducing kernel Hilbert spaces