An extremal problem for polynomials with nonnegative coefficients

Milovanović, Gradimir V.

doi:10.1090/S0002-9939-1985-0787886-8

An extremal problem for polynomials with nonnegative coefficients
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by Gradimir V. Milovanović PDF

Proc. Amer. Math. Soc. 94 (1985), 423-426 Request permission

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 ${C_n}(\alpha ) = {\sup _{P \in {W_n}}}{(\left \| {P’} \right \|/\left \| P \right \|)^2}$ is solved, which completes a result of A. K. Varma [7].

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