P.K. Suetin Technical University of Communication and Informatics, Moscow, Russia. Translated from the Russian by E.V. Pankratiev
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
This text includes the classification of differential equations which admits orthogonal polynomials as eigenfunctions and several two-dimensional analogies of classical orthogonal polynomials.
Klappentext
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.
