T. K. Pogany

Derivative uniform sampling via Weierstrass s(z). Truncation error analysis in [2,pi/ 2s²)

abstract:
In the entire functions space $\left[ 2,\frac{\pi q}{2s^2}\right)$ consisting of at most second order functions such that their type is less than $\pi q/(2s^2)$ it is valid the $q$-order derivative sampling series reconstruction procedure, reading at the von Neumann lattice $\{ s(m+ni)|\;(m,n)\in \bZ^2\}$ via the Weierstrass $\sigma(\cdot)$ as the sampling function, $s>0$. The uniform convergence of the sampling sums to the initial function is proved by the {\it circular truncation error} upper bound, especially derived for this reconstruction procedure. Finally, the explicit second and third order sampling formul{\ae} are given