Presenting a comprehensive theory of orthogonal polynomials in two real variables and properties of Fourier series in these polynomials, this volume also gives cases of orthogonality over a region and on a contour. The text includes the classification of differential equations which admits orthogonal polynomials as eigenfunctions and several two-dimensional analogies of classical orthogonal polynomials.

P.K. Suetin Technical University of Communication and Informatics, Moscow, Russia. Translated from the Russian by E.V. Pankratiev

Chapter I. General properties of polynomials orthogon all over a domain Chapter II. Some typical examples and special cases of orthogonality over a domain, Chapter III. Classical Appell's orthogon al polynomials, Chapter IV . Admissible differential equation for polynomials orthogon al over a domain, Chapter V . Potentially self-adjoint equation and Rodrigues formula Chapter V I. Harmonic polynomials orthogon al over a domain Chapter V II. Polynomials in two variables orthogon al on a contour Chapter V III. Generalized orthogon al polynomials in two Variables Chapter IX . Other results concerning the connection between orthogon alpolynomials and differential equations, Chapter X . Original results of T. Koornwinder, Chapter X I. Some recent results