Access the full text.
Sign up today, get DeepDyve free for 14 days.
(1944)
On polynomials orthogonal on the circle, on the trigonometric moment problem, and on allied Carathéodory and Schur functions
D. Khavinson, N. Stylianopoulos (2010)
Recurrence Relations for Orthogonal Polynomials and Algebraicity of Solutions of the Dirichlet Problem
P. Túrán (1975)
On orthogonal polynomialsAnalysis Mathematica, 1
J B Conway (2000)
Graduate Studies in Mmathematics, 21
M. Putinar, N. Stylianopoulos (2007)
Finite-Term Relations for Planar Orthogonal PolynomialsComplex Analysis and Operator Theory, 1
B Simon (2005)
American Mathematical Society Colloquium Publications, vol. 54
J. Conway (1999)
A course in operator theory
H. Hedenmalm (2002)
The dual of a bergman space on simply connected domainsJournal d’Analyse Mathématique, 88
Michael Dritschel (2001)
A COURSE IN OPERATOR THEORY (Graduate Studies in Mathematics 21)Bulletin of The London Mathematical Society, 33
D. Rolanía, G. Lagomasino (1999)
Ratio Asymptotics for Polynomials Orthogonal on Arcs of the Unit CircleConstructive Approximation, 15
H Hedenmalm (2002)
The dual of a Bergman space on simply connected domainsJ. Anal. Math., 88
K Astala, T Iwaniec, G Martin (2009)
Princeton Mathematical Series, vol. 48
R A Adams, J J F Fournier (2003)
Pure and Applied Mathematics (Amsterdam), vol. 140
D Khavinson, N Stylianopoulos (2009)
Around the Research of Vladimir Maz’ya II, International Mathematical Series, vol. 12
K. Astala, T. Iwaniec, G. Martin (2009)
Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (Pms-48)
W. Marsden (2012)
I and J
With the aid of Havin’s Lemma (which we generalize) we prove that polynomials orthogonal over the unit disk with respect to certain weighted area measures (Bergman polynomials) cannot satisfy a finite-term recurrence relation unless the weight is radial, in which case the polynomials are simply monomials. For polynomials orthogonal over the unit circle (Szegő polynomials) we provide a simple argument to show that the existence of a finite-term recurrence implies that the weight must be the reciprocal of the square modulus of a polynomial.
Computational Methods and Function Theory – Springer Journals
Published: Mar 21, 2012
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.