DC FieldValueLanguage
dc.contributor.authorBatra, Prashant-
dc.date.accessioned2020-11-20T12:13:23Z-
dc.date.available2020-11-20T12:13:23Z-
dc.date.issued2012-02-28-
dc.identifier.citationInternational Series of Numerical Mathematics (161): 67-86 (2012)de_DE
dc.identifier.isbn978-3-0348-0249-9de_DE
dc.identifier.isbn978-3-0348-0248-2de_DE
dc.identifier.issn2296-6072de_DE
dc.identifier.urihttp://hdl.handle.net/11420/7889-
dc.description.abstractNewton, Euler and many after them gave inequalities for real polynomials with only real zeros. We show how to extend classical inequalities ensuring a guaranteed minimal improvement. Our key is the construction of mappings with bounded image domains such that existing coefficient criteria from complex analysis are applicable. Our method carries over to the Laguerre-Pólya class 𝓛–𝓟 which contains real polynomials with exclusively real zeros and their uniform limits. The class 𝓛–𝓟 covers quasi-polynomials describing delay-differential inequalities as well as infinite convergent products representing entire functions, while it is at present not known whether the Riemann ξ-function belongs to this class. For the class 𝓛–𝓟 we obtain a new infinite family of inequalities which contains and generalizes the Laguerre-Turán inequalities.en
dc.language.isoende_DE
dc.subjectCoefficient inequalitiesde_DE
dc.subjectHankel determinantsde_DE
dc.subjectLogarithmic derivativede_DE
dc.subjectMoment problemde_DE
dc.subjectReality of zerosde_DE
dc.subject.ddc004: Informatikde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleDeriving inequalities in the laguerre-pólya class from properties of half-plane mappingsde_DE
dc.typeinBookde_DE
dc.type.dinibookPart-
dcterms.DCMITypeText-
tuhh.abstract.englishNewton, Euler and many after them gave inequalities for real polynomials with only real zeros. We show how to extend classical inequalities ensuring a guaranteed minimal improvement. Our key is the construction of mappings with bounded image domains such that existing coefficient criteria from complex analysis are applicable. Our method carries over to the Laguerre-Pólya class 𝓛–𝓟 which contains real polynomials with exclusively real zeros and their uniform limits. The class 𝓛–𝓟 covers quasi-polynomials describing delay-differential inequalities as well as infinite convergent products representing entire functions, while it is at present not known whether the Riemann ξ-function belongs to this class. For the class 𝓛–𝓟 we obtain a new infinite family of inequalities which contains and generalizes the Laguerre-Turán inequalities.de_DE
tuhh.publisher.doi10.1007/978-3-0348-0249-9_5-
tuhh.publication.instituteZuverlässiges Rechnen E-19de_DE
tuhh.type.opusInBuch (Kapitel / Teil einer Monographie)-
dc.type.driverbookPart-
dc.type.casraiBook Chapter-
tuhh.container.startpage67de_DE
tuhh.container.endpage86de_DE
tuhh.relation.ispartofseriesInternational Series of Numerical Mathematicsde_DE
tuhh.relation.ispartofseriesnumber161de_DE
dc.identifier.scopus2-s2.0-85089908361de_DE
local.status.inpressfalsede_DE
item.grantfulltextnone-
item.openairetypeinBook-
item.fulltextNo Fulltext-
item.languageiso639-1en-
item.creatorOrcidBatra, Prashant-
item.seriesrefInternational Series of Numerical Mathematics;161-
item.cerifentitytypePublications-
item.creatorGNDBatra, Prashant-
item.openairecristypehttp://purl.org/coar/resource_type/c_3248-
item.tuhhseriesidInternational Series of Numerical Mathematics-
crisitem.author.deptZuverlässiges Rechnen E-19-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
Appears in Collections:Publications without fulltext
Show simple item record

Page view(s)

23
Last Week
0
Last month
3
checked on Jan 17, 2021

Google ScholarTM

Check

Add Files to Item

Note about this record

Export

Items in TORE are protected by copyright, with all rights reserved, unless otherwise indicated.