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A method for generating multivariate multiple orthogonal polynomials
Lidia Fernández, Juan Antonio Villegas
In the framework of multiple orthogonal polynomials (MOPs) and their extension to the multivariate setting, a unified mechanism for generating structured families of multiple ortho…
A Rodrigues Formula for Multiple Orthogonal Polynomials on the Simplex
Lidia Fernández, Ana Foulquié-Moreno, Juan Antonio Villegas
Rodrigues formulas play a central role in the construction of orthogonal polynomials associated with classical measures. In this paper, we introduce a family of multivariate multip…
Multiple Orthogonal Polynomials of two real variables
Lidia Fernández, Juan Antonio Villegas
Polynomials known as Multiple Orthogonal Polynomials in a single variable are polynomials that satisfy orthogonality conditions concerning multiple measures and play a significant…
Compactly supported, orthogonal, continuous piecewise polynomial multiresolution analysis
Lidia Fernández, Jeffrey S. Geronimo, Plamen Iliev
We present explicit representations in terms of hypergeometric functions for the scaling functions in the orthogonal multiresolution analyses associated with piecewise contin…