On approximation of band-limited signals (Q918495)

The goal of this paper is to present some recent results on approximation of signals (functions) f: \({\mathcal R}\to {\mathcal C}\) in the class \[ B(\Omega_ 0)=\{\int^{\Omega_ 0}_{-\Omega_ 0}X(\Omega)\exp (i\Omega)d\Omega:\;X\in L_ 2(-\Omega_ 0,\Omega_ 0)\} \] on a given finite interval. The paper contains four parts. In the first one the error of an algorithm is defined. In the second one the average behavior of algorithms with respect to some probability measures on \(B(\Omega_ 0,\tau)\), where \(\tau\) is a positive number is investigated. The third part is an overview, and the fourth part contains new results.