Homogeneous polynomials and extensions of Hardy-Hilbert's inequality

Anagnostopoulos, VA; Sarantopoulos, Y; Tonge, AM

dc.contributor.author	Anagnostopoulos, VA	en
dc.contributor.author	Sarantopoulos, Y	en
dc.contributor.author	Tonge, AM	en
dc.date.accessioned	2014-03-01T02:09:18Z
dc.date.available	2014-03-01T02:09:18Z
dc.date.issued	2012	en
dc.identifier.issn	0025584X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29799
dc.subject	Hardy-Hilbert's inequality	en
dc.subject	Norm estimates	en
dc.subject	Permanents	en
dc.subject	Polynomials	en
dc.title	Homogeneous polynomials and extensions of Hardy-Hilbert's inequality	en
heal.type	journalArticle	en
heal.identifier.primary	10.1002/mana.201010035	en
heal.identifier.secondary	http://dx.doi.org/10.1002/mana.201010035	en
heal.publicationDate	2012	en
heal.abstract	If L is a continuous symmetric n-linear form on a real or complex Hilbert space and L̂ A is the associated continuous n-homogeneous polynomial, then \|\|L\|\| = \|\|L̂\|\|. We give a simple proof of this well-known result, which works for both real and complex Hilbert spaces, by using a classical inequality due to S. Bernstein for trigonometric polynomials. As an application, an open problem for the optimal lower bound of the norm of a homogeneous polynomial, which is a product of linear forms, is related to the so-called permanent function of an n × n positive definite Hermitian matrix. We have also derived generalizations of Hardy-Hilbert's inequality. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.	en
heal.journalName	Mathematische Nachrichten	en
dc.identifier.doi	10.1002/mana.201010035	en
dc.identifier.volume	285	en
dc.identifier.issue	1	en
dc.identifier.spage	47	en
dc.identifier.epage	55	en