Lidia Fernández

Lidia Fernández, Jeffrey S. Geronimo, Plamen Iliev

We present explicit representations in terms of hypergeometric functions for the scaling functions in the $C^0$ orthogonal multiresolution analyses associated with piecewise continuous polynomials. Closed formulas for the Mellin transform of these functions as well as their Fourier transforms are derived. Some new multiresolution analyses whose scaling functions have coefficients that are rational numbers are introduced and discussed.

Ruymán Cruz-Barroso, Lidia Fernández, Francisco Marcellán et al.

In this contribution we introduce a mixed interpolation-regression operator for functions defined in some domains of the plane. We focus the attention on the ellipse, an annulus and a polygon. An upper bound for such an operator is obtained. Cubature formulas for weight functions defined in such domains are studied. The performance of the above interpolation-regression methods is illustrated with some numerical examples taking into account the variations of the dimension of the interpolation and the regression part, respectively.