Orthogonal polynomials on the unit circle

In mathematics, orthogonal polynomials on the unit circle are families of polynomials that are orthogonal with respect to integration over the unit circle in the complex plane, for some probability measure on the unit circle. They were introduced by Szegő (1920, 1921, 1939).

The Rogers–Szegő polynomials are an examples of orthogonal polynomials on the unit circle.

References

• Koornwinder, Tom H.; Wong, Roderick S. C.; Koekoek, Roelof; Swarttouw, René F. (2010), "Orthogonal Polynomials on the unit circle", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F. et al., NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0521192255, MR2723248, http://dlmf.nist.gov/18.33 
• Simon, Barry (2005), Orthogonal polynomials on the unit circle. Part 1. Classical theory, American Mathematical Society Colloquium Publications, 54, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-3446-6, MR2105088, http://books.google.com/books?id=d94r7kOSnKcC 
• Simon, Barry (2005), Orthogonal polynomials on the unit circle. Part 2. Spectral theory, American Mathematical Society Colloquium Publications, 54, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-3675-0, MR2105089, http://books.google.com/books?id=54juCPc3ulwC 
• Szegő, Gábor (1920), "Beiträge zur Theorie der Toeplitzschen Formen", Mathematische Zeitschrift (Springer Berlin / Heidelberg) 6: 167–202, doi:10.1007/BF01199955, ISSN 0025-5874, http://dx.doi.org/10.1007/BF01199955 
• Szegő, Gábor (1921), "Beiträge zur Theorie der Toeplitzschen Formen", Mathematische Zeitschrift (Springer Berlin / Heidelberg) 9: 167–190, doi:10.1007/BF01279027, ISSN 0025-5874, http://dx.doi.org/10.1007/BF01279027 
• Szegő, Gábor (1939), Orthogonal Polynomials, Colloquium Publications, XXIII, American Mathematical Society, ISBN 978-0-8218-1023-1, MR0372517, http://books.google.com/books?id=3hcW8HBh7gsC