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.
1. General Properties of Polynomials Orthogonal Over a Domain 2. Some Typical Examples and Special Cases of Orthogonality Over a Domain 3. Classical Appell's Orthogonal Polynomials 4. Admissible Differential Equation for Polnomials Orthogonal Over a Domain 5. Potentially Self-Adjoint Equation and Rodrigues Formula 6. Harmonic Polynomials Orthogonal Over a Domain 7. Polynomials in Two Variables Orthogonal on a Contour 8. Generalized Orthogonal Polynomials in Two Variables 9. Other Results Concerning the Connection Between Orthogonal 10. Polynomials and Differential Equations 11. Original Results of T. Koornwinder Some Recent Results