Geodesic
Asymptotic properties of zeros of orthogonal trigonometric polynomials of half-integer orders
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 54-70

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For systems of orthogonal trigonometric polynomials of half-integer orders obtained by the Schmidt orthogonalization of the sequences $\cos(1/2)\tau$, $\sin(1/2)\tau$, $\cos(3/2)\tau$, $\sin(3/2)\tau$, $\cos(5/2)\tau$, $\sin(5/2)\tau,\dots$ and $\sin(1/2)\tau$, $\cos(1/2)\tau$, $\sin(3/2)\tau$, $\cos(3/2)\tau$, $\sin(5/2)\tau$, $\cos(5/2)\tau,\dots$ 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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     author = {V. M. Badkov},
     title = {Asymptotic properties of zeros of orthogonal trigonometric polynomials of half-integer orders},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {54--70},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a5/}
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V. M. Badkov. Asymptotic properties of zeros of orthogonal trigonometric polynomials of half-integer orders. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 54-70. http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a5/