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Derivative Uniform Sampling via Weierstrass σ(z). Truncation Error Analysis in
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Tibor K. Pogány
Veröffentlicht/Copyright:
23. Februar 2010
Abstract
In the entire functions space 
consisting of at most second order functions such that their type is less than πq/(2s2) it is valid the q-order derivative sampling series reconstruction procedure, reading at the von Neumann lattice {s(m + ni)| (m, n) ∈ 
} via the Weierstrass σ(·) as the sampling function, s > 0. The uniform convergence of the sampling sums to the initial function is proved by the circular truncation error upper bound, especially derived for this reconstruction procedure. Finally, the explicit second and third order sampling formulæ are given.
Key words and phrases:: Derivative sampling; entire functions spaces [ρ, σ]; [ρ, σ); Weierstrass sigma-function; plane sampling reconstruction; sampling circular truncation error upper bound
Received: 2000-10-09
Published Online: 2010-02-23
Published in Print: 2001-March
© Heldermann Verlag
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Schlagwörter für diesen Artikel
Derivative sampling;
entire functions spaces [ρ, σ];
[ρ, σ);
Weierstrass sigma-function;
plane sampling reconstruction;
sampling circular truncation error upper bound
Artikel in diesem Heft
- Polymersions of a Disk with Critical Points on the Boundary
- A Fixed Point Theorem of Leggett–Williams Type with Applications to Single- and Multivalued Equations
- Non-Noether Symmetries in Singular Dynamical Systems
- Weight Inequalities for Singular Integrals Defined on Spaces of Homogeneous and Nonhomogeneous Type
- Perturbation of a Fredholm Complex by Inessential Operators
- Weighted Exponential Inequalities
- On the Representation of Numbers by the Direct Sums of Some Quaternary Quadratic Forms
- On Local Invariants of Totally Real Surfaces
- On the Number of Representations of Positive Integers by the Quadratic Form
- Derivative Uniform Sampling via Weierstrass σ(z). Truncation Error Analysis in
- On Periodic Solutions of Autonomous Difference Equations
- Inequalities of Calderon–Zygmund Type for Trigonometric Polynomials
- Hilbert Spaces Formed by Strongly Harmonizable Stable Processes
- Optimal Mean-Variance Robust Hedging under Asset Price Model Misspecification
