(2019) Marcellán, Francisco; Marriaga, Misael E.; Pérez, T. E.; Piñar, M. A.
Coherent pairs of measures were introduced in 1991 and constitute a very useful
tool in the study of Sobolev orthogonal polynomials on the real line. In this work,
coherence and partial coherence in two variables appear as the natural extension of
the univariate case. Given two families of bivariate orthogonal polynomials expressed
as polynomial systems, they are a partial coherent pair if there exists a polynomials of
the second family can be given as a linear combination of the _x001C_rst partial derivatives
of (at most) three consecutive polynomials of the _x001C_rst family. A full coherent pair
is a pair of families of bivariate orthogonal polynomials related by means of partial
coherent relations in each variable. Consequences of this kind of relations concerning
both families of bivariate orthogonal polynomials are studied.