Bivariate Generalized Exponential Sampling Series and Applications to Seismic Waves

Abstract

In this paper, we introduce the generalized exponential sampling series of bivariate functions and establish some pointwise and uniform convergence results, also in a quantitative form. Moreover, we study the pointwiseasymptotic behaviour of the series. One of the basic tools is the Mellin–Taylor formula for bivariate functions, hereintroduced. A practical application to seismic waves is also outlined.