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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 2, Pages 54–70
(Mi timm932)
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Asymptotic properties of zeros of orthogonal trigonometric polynomials of half-integer orders
V. M. Badkovab a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University
Abstract:
For systems of orthogonal trigonometric polynomials of half-integer orders obtained by the Schmidt orthogonalization of the sequences cos(1/2)τ, sin(1/2)τ, cos(3/2)τ, sin(3/2)τ, cos(5/2)τ, sin(5/2)τ,… and sin(1/2)τ, cos(1/2)τ, sin(3/2)τ, cos(3/2)τ, sin(5/2)τ, cos(5/2)τ,… in the measure dσ(τ) on [0,2π], we study the connections with the system of polynomials that is orthogonal on the unit circle in the same measure. An asymptotic formula is obtained for zeros of a trigonometric polynomial of half-integer order that is orthogonal with an even weight satisfying the Bernstein–Szego condition.
Keywords:
trigonometric polynomials, orthogonality, asymptotics of zeros.
Received: 29.12.2012
Citation:
V. M. Badkov, “Asymptotic properties of zeros of orthogonal trigonometric polynomials of half-integer orders”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 2, 2013, 54–70
Linking options:
https://www.mathnet.ru/eng/timm932 https://www.mathnet.ru/eng/timm/v19/i2/p54
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Abstract page: | 293 | Full-text PDF : | 88 | References: | 54 | First page: | 4 |
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