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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Comments on an $ L\sp 2$ inequality of A. K. Varma involving the first derivative of polynomials


Author: Li-Chien Shen
Journal: Proc. Amer. Math. Soc. 111 (1991), 955-959
MSC: Primary 26D15
MathSciNet review: 1039265
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Abstract: Let $ {t_n}$ be a trigonometric polynomial of degree $ n$ with real coefficients, and let $ w\left( x \right) \in {C^2}\left[ {0,\pi } \right]$ be nonnegative. Employing a well-known result of G. Szegö, we study the extremal property of the integral

$\displaystyle \int_0^\pi {{{\left( {{{t'}_n}\left( x \right)} \right)}^2}w\left( x \right)dx} ,$

subject to the constraint $ {\left\Vert {{t_n}} \right\Vert _\infty } \leq 1$.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1039265-9
PII: S 0002-9939(1991)1039265-9
Article copyright: © Copyright 1991 American Mathematical Society