Asymptotic properties of general orthogonal polynomials

1939 ◽  
pp. 296-312
Keyword(s):  
Orthogonal Polynomials ◽  
Asymptotic Properties

scholarly journals Some asymptotic properties for orthogonal polynomials with respect to varying measures

2005 ◽  
Vol 135 (1) ◽  
pp. 22-34 ◽  
Author(s):  
María Pilar Alfaro ◽  
Manuel Bello Hernández ◽  
Jesús María Montaner ◽  
Juan L. Varona
Keyword(s):  
Orthogonal Polynomials ◽  
Asymptotic Properties

scholarly journals Asymptotic properties of generalized Laguerre orthogonal polynomials

2004 ◽  
Vol 15 (2) ◽  
pp. 151-165 ◽  
Author(s):  
Renato Álvarez-Nodarse ◽  
Juan J. Moreno-Balcázar
Keyword(s):  
Orthogonal Polynomials ◽  
Asymptotic Properties

Comportement asymptotique des marches aleatoires associees aux polynomes de Gegenbauer et applications

1984 ◽  
Vol 16 (2) ◽  
pp. 293-323 ◽  
Author(s):  
Leonard Gallardo
Keyword(s):  
Fourier Transform ◽  
Markov Chains ◽  
Asymptotic Behaviour ◽  
Random Walks ◽  
Orthogonal Polynomials ◽  
Comparison Theorem ◽  
Asymptotic Properties ◽  
Basic Tool ◽  
Independent Increments ◽  
Gegenbauer’S Polynomials

Random walks on N associated with orthogonal polynomials have properties similar to classical random walks on . In fact such processes have independent increments with respect to a hypergroup structure on with a convolution and a Fourier transform which is the basic tool for their study. We illustrate these ideas by giving a description of the asymptotic behaviour (CLT and ILL) of the random walks associated with Gegenbauer's polynomials. Moreover we can then use these random walks as a reference scale to deduce asymptotic properties of other Markov chains on via a comparison theorem which is of independent interest.

scholarly journals On asymptotic properties of Freud–Sobolev orthogonal polynomials

2003 ◽  
Vol 125 (1) ◽  
pp. 26-41 ◽  
Author(s):  
Alicia Cachafeiro ◽  
Francisco Marcellán ◽  
Juan J. Moreno-Balcázar
Keyword(s):  
Orthogonal Polynomials ◽  
Asymptotic Properties ◽  
Sobolev Orthogonal Polynomials
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