Applications of new Geronimus type identities for real orthogonal polynomials

Author:
D. S. Lubinsky

Journal:
Proc. Amer. Math. Soc. **138** (2010), 2125-2134

MSC (2010):
Primary 42C05; Secondary 41A17, 41A10, 41A55

Published electronically:
February 3, 2010

MathSciNet review:
2596051

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a positive measure on the real line, with associated orthogonal polynomials . Let Im. Then there is an explicit constant such that for all polynomials of degree at most ,

**1.**Louis de Branges,*Hilbert spaces of entire functions*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1968. MR**0229011****2.**G. Freud,*Orthogonal Polynomials*, Pergamon Press/Akademiai Kiado, Budapest, 1971.**3.**Denis Krutikov and Christian Remling,*Schrödinger operators with sparse potentials: asymptotics of the Fourier transform of the spectral measure*, Comm. Math. Phys.**223**(2001), no. 3, 509–532. MR**1866165**, 10.1007/s002200100552**4.**D. S. Lubinsky,*Universality limits for random matrices and de Branges spaces of entire functions*, J. Funct. Anal.**256**(2009), no. 11, 3688–3729. MR**2514057**, 10.1016/j.jfa.2009.02.021**5.**Barry Simon,*Orthogonal polynomials on the unit circle. Part 1*, American Mathematical Society Colloquium Publications, vol. 54, American Mathematical Society, Providence, RI, 2005. Classical theory. MR**2105088****6.**Barry Simon,*Orthogonal polynomials with exponentially decaying recursion coefficients*, Probability and mathematical physics, CRM Proc. Lecture Notes, vol. 42, Amer. Math. Soc., Providence, RI, 2007, pp. 453–463. MR**2352283**

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Additional Information

**D. S. Lubinsky**

Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160

Email:
lubinsky@math.gatech.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-10-10276-7

Keywords:
Orthogonal polynomials on the real line,
Geronimus formula,
discrepancy,
weak convergence,
Gauss quadrature

Received by editor(s):
August 17, 2009

Received by editor(s) in revised form:
October 22, 2009

Published electronically:
February 3, 2010

Additional Notes:
This research was supported by NSF grant DMS0700427 and U.S.-Israel BSF grant 2004353

Communicated by:
Walter Van Assche

Article copyright:
© Copyright 2010
American Mathematical Society