ON THE ASYMPTOTIC STABILITY OF THE ULTRASPHERICAL OPERATORS

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HESHMATI G.S.

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Journal: Year:2003 | Volume:36 | Issue:4 (78) Page(s): 477-482

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Information Journal Paper

Title

ON THE ASYMPTOTIC STABILITY OF THE ULTRASPHERICAL OPERATORS

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HESHMATI G.S. | Issue Writer Certificate

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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

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APA: Copy

HESHMATI, G.S.. (2003). ON THE ASYMPTOTIC STABILITY OF THE ULTRASPHERICAL OPERATORS. JOURNAL OF FACULTY OF ENGINEERING (UNIVERSITY OF TEHRAN), 36(4 (78)), 477-482. SID. https://sid.ir/paper/14277/en

Vancouver: Copy

HESHMATI G.S.. ON THE ASYMPTOTIC STABILITY OF THE ULTRASPHERICAL OPERATORS. JOURNAL OF FACULTY OF ENGINEERING (UNIVERSITY OF TEHRAN)[Internet]. 2003;36(4 (78)):477-482. Available from: https://sid.ir/paper/14277/en

IEEE: Copy

G.S. HESHMATI, “ON THE ASYMPTOTIC STABILITY OF THE ULTRASPHERICAL OPERATORS,” JOURNAL OF FACULTY OF ENGINEERING (UNIVERSITY OF TEHRAN), vol. 36, no. 4 (78), pp. 477–482, 2003, [Online]. Available: https://sid.ir/paper/14277/en

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