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Derivative Uniform Sampling via Weierstrass σ(z). Truncation Error Analysis in
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Tibor K. Pogány
Published/Copyright:
February 23, 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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