Two Variable Deformations of the Chebyshev Measure

The general theory of bivariate orthogonal polynomials goes back to the work of Jackson [12]. Special examples have arisen in studies related to symmetric groups [4, 16, 22]), as extensions of one variable polynomials [7, 15] and as eigenfunctions of partial differential equations [19, 14, 13, 21]. An updated account of the theory can be found in the books [5, 25]. A major difficulty encountered in the theory of orthogonal polynomials of more than one variable is which monomial ordering to use. Starting with [12], the preferred ordering is the total degree ordering and for polynomials with the same total degree the ordering is lexicographical that is