An abstract approach to sampling type operators inspired by the work of P.L. Butzer. Part I- Linear Operators

Here a new approach to the study of approximation problems by means of a family of linear integral operators is presented. The abstract approach used, which is based mainly on the use of locally compact topological groups, allows us to give a unifying method in order to study a large class of approximation problems and, as an application to signal processing, in the setting of modular spaces we obtain the recosntruction of signals which can be discontinuous and are not necessarily of finite energy or band-limited.