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 Trudy Inst. Mat. i Mekh. UrO RAN, 2013, Volume 19, Number 2, Pages 54–70 (Mi timm932)

Asymptotic properties of zeros of orthogonal trigonometric polynomials of half-integer orders

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 $\cos(1/2)\tau$, $\sin(1/2)\tau$, $\cos(3/2)\tau$, $\sin(3/2)\tau$, $\cos(5/2)\tau$, $\sin(5/2)\tau,…$ and $\sin(1/2)\tau$, $\cos(1/2)\tau$, $\sin(3/2)\tau$, $\cos(3/2)\tau$, $\sin(5/2)\tau$, $\cos(5/2)\tau,…$ in the measure $d\sigma(\tau)$ on $[0,2\pi]$, 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.

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Bibliographic databases:
UDC: 517.587+517.518.865+517.15

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

Citation in format AMSBIB
\Bibitem{Bad13} \by V.~M.~Badkov \paper Asymptotic properties of zeros of orthogonal trigonometric polynomials of half-integer orders \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2013 \vol 19 \issue 2 \pages 54--70 \mathnet{http://mi.mathnet.ru/timm932} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3363373} \elib{http://elibrary.ru/item.asp?id=19053968}