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


An extremal problem for polynomials with nonnegative coefficients

Author: Gradimir V. Milovanović
Journal: Proc. Amer. Math. Soc. 94 (1985), 423-426
MSC: Primary 26C05; Secondary 41A17
MathSciNet review: 787886
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Abstract: Let $ {W_n}$ be the set of all algebraic polynomials of exact degree $ n$ whose coefficients are all nonnegative. For the norm in $ {L^2}[0,\infty )$ with generalized Laguerre weight function $ w(x) = {x^\alpha }{e^{ - x}}\quad (\alpha > - 1)$, the extremal problem $ {C_n}(\alpha ) = {\sup _{P \in {W_n}}}{(\left\Vert {P'} \right\Vert/\left\Vert P \right\Vert)^2}$ is solved, which completes a result of A. K. Varma [7].

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PII: S 0002-9939(1985)0787886-8
Article copyright: © Copyright 1985 American Mathematical Society

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