Generalizations of Goncalves' inequality

dc.creator	Borwein, Peter
dc.creator	Mossinghoff, Michael J.
dc.creator	Vaaler, Jeffrey D.
dc.date	2005-01-11
dc.date.accessioned	2026-07-07T05:15:58Z
dc.date.available	2026-07-07T05:15:58Z
dc.description	If $F$ is a polynomial with complex coefficients, leading term $a_N$, and roots $α_1$, ..., $α_N$, then Gonçalves' inequality states that $\\|F\\|_2^2$ is bounded below by $\abs{a_N}^2 (\prod_{n=1}^N \max\{1, \abs{α_n}^2\} + \prod_{n=1}^N \min\{1, \abs{α_n}^2\})$. We establish generalizations of this inequality for other $L_p$ norms, and derive additional lower bounds on the $L_p$ norms of a polynomial in terms of its coefficients.
dc.description	9 pages
dc.identifier	https://arxiv.org/abs/math/0501163
dc.identifier	http://arxiv.org/abs/math/0501163
dc.identifier.uri	http://salesiana.dossiersoluciones.com/handle/123456789/73819
dc.subject	Classical Analysis and ODEs
dc.subject	Number Theory
dc.subject	30A10, 30C10 (Primary) 26D05, 42A05 (Secondary)
dc.title	Generalizations of Goncalves' inequality
dc.type	text

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