engleski

Truncation error upper bounds in derivative Whittaker-type plane sampling reconstruction

A survey is presented on the author's mean square and almost sure Whittaker-type derivative sampling theorems obtained for the class L^alpha(Omega, F, P), 0 <= alpha <= 2 of stochastic processes having spectral representation, with the aid of the Weierstrass sigma-function. Processes of this class are represented by interpolation series. The results are valid for harmonizable and weakly stationary (or in the Hinčin sense stationary) processes (alpha =2) as well. The formulae are interpreted in the alpha-mean and also almost sure sense when the input function and its derivatives are sampled at the points of the integer lattice Z^2. The circular truncation error is introduced and used in the truncation error analysis and related sampling sum convergence rates are shown.

Circular truncation error ; Derivative sampling ; Leont'ev spaces of entire functions ; Piranashvili-type stochastic processes ; Truncation error upper bounds ; Weierstrass sigma-function ; Whittaker-type sampling ; (p, q)-order weighted differential operator

nije evidentirano