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Universal truncation error upper bounds in sampling restoration
-
Andriy Ya. Olenko
and
Tibor K. Pogány
Published/Copyright:
October 21, 2010
Abstract
Universal (pointwise uniform and time shifted) truncation error upper bounds are presented for the Whittaker–Kotel'nikov–Shannon sampling restoration sum for Bernstein function classes 
, q > 1, d ∈ ℕ, when the decay rate of the sample functions is unknown. The case of regular sampling is discussed. Extremal properties of the related series of sinc functions are investigated.
Keywords.: Whittaker–Kotel'nikov–Shannon sampling restoration formula; approximation/interpolation error level; Plancherel–Pólya inequality; Bernstein function class; regular sampling theorem; truncation error upper bound; multidimensional sampling; sinc functions; incomplete Lambda function
Received: 2008-11-07
Revised: 2009-06-11
Published Online: 2010-10-21
Published in Print: 2010-December
© de Gruyter 2010
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Keywords for this article
Whittaker–Kotel'nikov–Shannon sampling restoration formula;
approximation/interpolation error level;
Plancherel–Pólya inequality;
Bernstein function class;
regular sampling theorem;
truncation error upper bound;
multidimensional sampling;
sinc functions;
incomplete Lambda function
Articles in the same Issue
- On a problem concerning quaternion valued Gaussian random variables
- Mazur–Ulam theorem for Riesz spaces
- A limit theorem on symmetric matrices
- On a relationship between the measurability and continuity of real-valued functions
- Proof of the Zalcman conjecture for initial coefficients
- Recursive parameter estimation in the trend coefficient of a diffusion process
- Backward stochastic PDEs related to the utility maximization problem
- On the statistical estimation of the logarithmic derivative of a measure in a Hilbert space
- Asymptotic efficiency of exponentiality tests based on order statistics characterization
- Universal truncation error upper bounds in sampling restoration
- An operator version of Abel's continuity theorem
