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On some inequalities involving the zeros and weighted norms of polynomials

Author(s): Li-Chien Shen
Journal: Proc. Amer. Math. Soc. 130 (2002), 53-57.
MSC (2000): Primary 30C10, 41A17
Posted: May 3, 2001
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Abstract | References | Similar articles | Additional information

Abstract:

Using Parseval's identity and the Hardy-Littlewood-Pólya inequality on the maximal decreasing rearrangement, we establish some sharp inequalities involving the weighted norm and the zeros of polynomials.

References:

1.: A.Kroo and I.Pritsker, A sharp version of Mahler's inequality for products of polynomials, Bull. London Math. Soc. 31(1999), 269-278. MR 99m:30008
2.: G.H.Hardy, J.E.Littlewood, and G.Pólya, Inequalities, Cambridge University Press, New York, 1934. 1952 edition MR 13:727e; 1988 edition MR 89d:26016


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