Reconstrucción Estable: ¿Bases o Pseudobases?

Abstract

The reconstruction of a function f from a set of data (the coefficients of f in some suitable basis) becomes a problem of a "good" caracterization of the space in terms of the coefficients.
There exist different types of basis with many properties; in each problem we have to choose the ones that best fit the problem at hand. Here we present an overview of the many generating families and its properties. We rather emphasize examples than proof of results. We end up with a comparison between the new wavelet basis and the classical Fourier basis.