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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1976, Volume 19, Issue 5, Pages 659–672 (Mi mz7786)

The asymptotic representation at a point of the derivative of orthonormal polynomials

B. L. Golinskii

Khar'kov Aviation Institute

Abstract: A theorem is proved on the asymptotic representation at the pointe $e^{i\theta_0}$ of the first derivative of polynomials, orthonormal on the unit circumference, under the following conditions: the weight $\varphi(\theta)$ is bounded from above, the function $\varphi^{-2}(\theta)$ is summable on the segment $[-\pi,\pi]$; at the $\eta_0$ neighborhood of the point $\theta=\theta_0$ the weight is bounded from below by a positive constant and has a bounded variation; the trigonometric conjugate $\widetilde{\ln\varphi(\theta_0)}$ exists. These restrictions are less restrictive than those in Ch. Hörup's similar theorem.

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English version:
Mathematical Notes, 1976, 19:4, 397–404

Bibliographic databases:

UDC: 517.5

Citation: B. L. Golinskii, “The asymptotic representation at a point of the derivative of orthonormal polynomials”, Mat. Zametki, 19:5 (1976), 659–672; Math. Notes, 19:4 (1976), 397–404

Citation in format AMSBIB
\Bibitem{Gol76} \by B.~L.~Golinskii \paper The asymptotic representation at a point of the derivative of orthonormal polynomials \jour Mat. Zametki \yr 1976 \vol 19 \issue 5 \pages 659--672 \mathnet{http://mi.mathnet.ru/mz7786} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=422985} \zmath{https://zbmath.org/?q=an:0348.42010|0343.42007} \transl \jour Math. Notes \yr 1976 \vol 19 \issue 4 \pages 397--404 \crossref{https://doi.org/10.1007/BF01142559}