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.
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