Access the full text.
Sign up today, get DeepDyve free for 14 days.
Tivadar Danka (2016)
Universality limits for generalized Jacobi measuresarXiv: Classical Analysis and ODEs
F. Peherstorfer, R. Steinbauer (2000)
Orthogonal Polynomials on the Circumference and Arcs of the CircumferenceJournal of Approximation Theory, 102
(2020)
Orthogonal Polynomials on the Unit CircleEncyclopedia of Special Functions: The Askey-Bateman Project
Feruenc Pinte'r, P. Nevai (1995)
Schur functions and orthogonal polynomials on the unit circlearXiv: Classical Analysis and ODEs
E. Levin, D. Lubinsky (2007)
Universality Limits Involving Orthogonal Polynomials on the Unit CircleComputational Methods and Function Theory, 7
(2002)
Bessel Functions and Their Applications, Translated from the Russian by E
A. Máté, P. Nevai, V. Totik (1991)
Szegö’s extremum problem on the unit circleAnnals of Mathematics, 134
J. Geronimo, W. Assche (1988)
ORTHOGONAL POLYNOMIALS ON SEVERAL INTERVALS VIA A POLYNOMIAL MAPPINGTransactions of the American Mathematical Society, 308
J. Keating, N. Snaith (2003)
Random matrices and L-functionsJournal of Physics A, 36
F. Peherstorfer, R. Steinbauer (1997)
Asymptotic Behaviour of Orthogonal Polynomials on the Unit Circle with Asymptotically Periodic Reflection CoefficientsJournal of Approximation Theory, 105
J McLaughlin (2004)
Combinatorial identities deriving from theIntegers: Electr. J. Combin. Number Theory, 4
F Pintér, P Nevai (1996)
Schur functions and orthogonal polynomials on the unit circle, in ?Approximation Theory and Function Series?Bolyai Soc. Math. Stud., 5
Jairo Charris, M. Ismail, Sergio Monsalve (1994)
On sieved orthogonal polynomials. X. General blocks of recurrence relations.Pacific Journal of Mathematics, 163
(2008)
The Christoffel-Darboux kernel, in Perspectives in partial differential equations, harmonic analysis and applications
B. Simon (2007)
Fine Structure of the Zeros of Orthogonal Polynomials: A Review
(1940)
Sur quelques équations aux différences finies et les systèmes correspondants des polynômes orthogonaux
MEH Ismail (2005)
Classical and Quantum Orthogonal Polynomials
M. Cantero (2013)
From Orthogonal Polynomials on the Unit Circle to Functional Equations via Generating Functions
D. Lubinsky (2010)
Universality Limits at the Hard Edge of the Spectrum for Measures with Compact SupportInternational Mathematics Research Notices, 2008
Brian Simanek (2017)
Universality at an Endpoint for Orthogonal Polynomials with Geronimus-Type WeightsarXiv: Classical Analysis and ODEs
J. Laughlin, Nancy Wyshinski (2006)
Further combinatorial identities deriving from the nth power of a 2×2 matrixDiscret. Appl. Math., 154
F. Peherstorfer, R. Steinbauer (2000)
Strong Asymptotics of Orthonormal Polynomials with the Aid of Green's FunctionSIAM J. Math. Anal., 32
B. Simon (2004)
Fine structure of the zeros of orthogonal polynomials III: Periodic recursion coefficientsCommunications on Pure and Applied Mathematics, 59
F. Peherstorfer, R. Steinbauer (2000)
Asymptotic Behaviour of Orthogonal Polynomials on the Unit Circle with Asymptotically Periodic Reflection Coefficients: II. Weak Asymptotics☆☆☆Journal of Approximation Theory, 105
F. Peherstorfer, R. Steinbauer (1996)
Orthogonal Polynomials on Arcs of the Unit Circle: II. Orthogonal Polynomials with Periodic Reflection CoefficientsJournal of Approximation Theory, 87
T Danka, V Totik (2018)
Christoffel functions with power type weightsJ. Eur. Math. Soc., 20
Brian Simanek (2016)
Two universality results for polynomial reproducing kernelsJ. Approx. Theory, 216
A. Lukashov (2004)
Circular parameters of polynomials orthogonal on several arcs of the unit circleSbornik Mathematics, 195
M. Ismail, Xin Li (1992)
On sieved orthogonal polynomials. IX. Orthogonality on the unit circle.Pacific Journal of Mathematics, 153
P. Borwein, T. Erdélyi (1995)
Polynomials and Polynomial Inequalities
C. Brezinski (1980)
General orthogonal polynomials
B Simon (2005)
Orthogonal Polynomials on the Unit Circle, Part Two: Spectral Theory
B. Simon (2010)
Szegő's Theorem and Its Descendants: Spectral Theory for L 2 Perturbations of Orthogonal Polynomials
T Danka (2017)
Universality limits for generalized Jacobi measuresAdv. Math., 316
Jairo Charris, M. Ismail (1993)
Sieved orthogonal polynomials. VII. Generalized polynomial mappingsTransactions of the American Mathematical Society, 340
J. Geronimo, W. Assche (1986)
Orthogonal polynomials with asymptotically periodic recurrence coefficientsJournal of Approximation Theory, 46
Tivadar Danka, V. Totik (2015)
Christoffel functions with power type weightsarXiv: Classical Analysis and ODEs
D. Lubinsky, V. Nguyen (2013)
Universality Limits involving Orthogonal Polynomials on an Arc of the Unit CircleComputational Methods and Function Theory, 13
M. Jesus, J. Petronilho (2010)
On orthogonal polynomials obtained via polynomial mappingsJ. Approx. Theory, 162
F. Peherstorfer, R. Steinbauer (1996)
Orthogonal Polynomials on Arcs of the Unit Circle, IJournal of Approximation Theory, 85
B Simanek (2018)
Universality at an endpoint for orthogonal polynomials with Geronimus-type weightsProc. Am. Math. Soc., 146
B. Simon (2004)
Ratio asymptotics and weak asymptotic measures for orthogonal polynomials on the real lineJ. Approx. Theory, 126
B Simon (2005)
Orthogonal Polynomials on the Unit Circle, Part One: Classical Theory
Brian Simanek (2013)
The Bergman Shift Operator on Polynomial LemniscatesConstructive Approximation, 41
A Lukashov (2004)
Circular parameters of polynomials that are orthogonal on several arcs of the unit circleMat. Sb., 195
V. Totik (2009)
Universality and fine zero spacing on general setsArkiv för Matematik, 47
B Simon (2011)
Szeg??s Theorem and Its Descendants, Spectral Theory for
We find a new formula for the orthonormal polynomials corresponding to a measure $$\mu $$ μ on the unit circle whose Verblunsky coefficients are periodic. The formula is presented using the Chebyshev polynomials of the second kind and the discriminant of the periodic sequence. We present several applications including a resolution of a problem suggested by Simon (Commun Pure Appl Math 59(7):1042–1062, 2006) regarding the existence of singular points in the bands of the support of the measure and a universality result at all points of the essential support of $$\mu $$ μ .
Research in the Mathematical Sciences – Springer Journals
Published: Oct 19, 2018
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.