7 papers
Symmetric Jacobi Polynomials on a Triangle and Their Spectral Algebra
Misael E. Marriaga, Miguel A. Piñar
We study a family of symmetric orthogonal polynomials on the unit triangle associated with the weight \[ w_{α,γ,κ}(x,y) = (xy)^α(1-x-y)^γ|x-y|^{2κ+1}, \quad α,γ,κ>-1,\quad α+κ>-\fr…
A class of Truncated Freud polynomials
Juan Carlos García-Ardila, Francisco Marcellán, Misael E. Marriaga
Consider the following truncated Freud linear functional depending on a parameter , The…
Ladder operators for generalized Zernike or disk polynomials
Misael E. Marriaga
The aim of this work is to report on several ladder operators for generalized Zernike polynomials which are orthogonal polynomials on the unit disk $\mathbf{D}\,=\,\{(x,y)\in \math…
On classical orthogonal polynomials and the Cholesky factorization of a class of Hankel matrices
Misael E. Marriaga, Guillermo Vera de Salas, Marta Latorre +1
Classical moment functionals (Hermite, Laguerre, Jacobi, Bessel) can be characterized as those linear functionals whose moments satisfy a second order linear recurrence relation. I…
A class of Bernstein-type operators on the unit disk
Marlon J. Recarte, Misael E. Marriaga, Teresa E. Pérez
We construct and study sequences of linear operators of Bernstein-type acting on bivariate functions defined on the unit disk. To this end, we study Bernstein-type operators under…
Three term relations for a class of bivariate orthogonal polynomials
Misael Marriaga, Teresa E. Pérez, Miguel A. Piñar
We study matrix three term relations for orthogonal polynomials in two variables constructed from orthogonal polynomials in one variable. Using the three term recurrence relation f…
Matrix Pearson equations satisfied by Koornwinder weights in two variables
Francisco Marcellán, Misael E. Marriaga, Teresa E. Pérez +1
We consider Koornwinder's method for constructing orthogonal polynomials in two variables from orthogonal polynomials in one variable. If semiclassical orthogonal polynomials in on…