Über einige zweidimensionale Analoga der klassischen orthogonalen Polynome

Abstract

The paper deals with some families of polynomials in two variables-eigenfunctions of a linear operator in partial derivates of second order with polynomial coefficients. These polynomials have certain orthogonality properties with respect to a scalar product defined in the space of polynomials by means of a double sequence of moments. In greater detail is investigated a special class of operators when the corresponding polynomials form two biorthogonal sequences analogical to the classical orthogonal polynomials. An enumeration of all operators belonging to the special class is given.