Semi‐discrete operators in multivariate setting: Convergence properties and applications

Abstract

In this paper, we study the convergence properties of certain semi‐discrete exponential‐type sampling series in a multidimensional frame. In particular, we obtain an asymptotic formula of Voronovskaya type, which gives a precise order of approximation in the space of continuous functions, and we give some particular example illustrating the theory. Applications to the study of the seismic waves are illustrated.