Paper Information

Journal:   JOURNAL OF FACULTY OF ENGINEERING (UNIVERSITY OF TEHRAN)   March 2003 , Volume 36 , Number 4 (78); Page(s) 477 To 482.
 
Paper: 

ON THE ASYMPTOTIC STABILITY OF THE ULTRASPHERICAL OPERATORS

 
 
Author(s):  HESHMATI G.S.*
 
* Dept. of Engineering Science Faculty of Engineering University of Tehran
 
Abstract: 

The ultra spherical polynomials form a orthogonal system on I=[-1,1] for the measure dμα(x)=(1-x2)α dx for α>-1/2 . The Gegenbauer's multiplication formula shows that the Gegenbauer Kernel is stochastic. By means of the Gegenbauer Kernel we construct a Markov operator Pα,x and by using the abstract result for a Markov Operators we prove its asymptotic stability for o α ≤1/2. This result will be generalized for all α≥1/2 by use of the Harmonic analysis techniques

 
Keyword(s): 
 
References: 
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