scholarly journals Asymptotics for orthogonal polynomials off the circle

2004 ◽  
Vol 2004 (1) ◽  
pp. 37-53
Author(s):  
R. Khaldi ◽  
R. Benzine
Keyword(s):  
Orthogonal Polynomials ◽  
Fixed Points ◽  
Unit Circle ◽  
Positive Measure ◽  
Asymptotic Formulas ◽  
Strong Asymptotics ◽  
Asymptotics Of Orthogonal Polynomials ◽  
The Masses

We study the strong asymptotics of orthogonal polynomials with respect to a measure of the typedμ/2π+∑j=1∞Ajδ(z−zk), whereμis a positive measure on the unit circleΓsatisfying the Szegö condition and{zj}j=1∞are fixed points outsideΓ. The masses{Aj}j=1∞are positive numbers such that∑j=1∞Aj<+∞. Our main result is the explicit strong asymptotic formulas for the corresponding orthogonal polynomials.

scholarly journals ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS VIA RECURRENCE RELATIONS

2012 ◽  
Vol 10 (02) ◽  
pp. 215-235 ◽  
Author(s):  
X.-S. WANG ◽  
R. WONG
Keyword(s):  
Orthogonal Polynomials ◽  
Legendre Polynomials ◽  
Recurrence Relations ◽  
Hermite Polynomials ◽  
Asymptotic Formulas ◽  
Systematic Technique ◽  
Asymptotics Of Orthogonal Polynomials

We use the Legendre polynomials and the Hermite polynomials as two examples to illustrate a simple and systematic technique on deriving asymptotic formulas for orthogonal polynomials via recurrence relations. Another application of this technique is to provide a solution to a problem recently raised by M. E. H. Ismail.

scholarly journals Strong asymptotics for the Pollaczek multiple orthogonal polynomials

2015 ◽  
Vol 92 (3) ◽  
pp. 709-713
Author(s):  
A. I. Aptekarev ◽  
G. López Lagomasino ◽  
A. Martínez-Finkelshtein
Keyword(s):  
Orthogonal Polynomials ◽  
Strong Asymptotics ◽  
Multiple Orthogonal Polynomials

Multiple Orthogonal Polynomials on the Unit Circle

2007 ◽  
Vol 28 (2) ◽  
pp. 173-197 ◽  
Author(s):  
Judit Minguez Ceniceros ◽  
Walter Van Assche
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Multiple Orthogonal Polynomials
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