Topics in matrix analysis
On multivariate orthogonal polynomials
SIAM Journal on Mathematical Analysis
Orthogonal polynomials in two variables and second-order partial differential equations
ICCAM '96 Proceedings of the seventh international congress on Computational and applied mathematics
Partial differential equations having orthogonal polynomial solutions
Journal of Computational and Applied Mathematics
Second order partial differential equations for gradients of orthogonal polynomials in two variables
Journal of Computational and Applied Mathematics - Special issue: Special functions in harmonic analysis and applications
Semiclassical orthogonal polynomials in two variables
Journal of Computational and Applied Mathematics
A matrix Rodrigues formula for classical orthogonal polynomials in two variables
Journal of Approximation Theory
Bivariate orthogonal polynomials in the Lyskova class
Journal of Computational and Applied Mathematics
New steps on Sobolev orthogonality in two variables
Journal of Computational and Applied Mathematics
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Orthogonal polynomials in two variables constitute a very old subject in approximation theory. Usually they are studied as solutions of second-order partial differential equations. In this work, we study two-variable orthogonal polynomials associated with a moment functional satisfying the two-variable analogue of the Pearson differential equation. From this approach, we derive the extension of some of the usual characterizations of the classical orthogonal polynomials in one variable.