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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorESTERLE, Jean
dc.date.accessioned2024-04-04T03:18:32Z
dc.date.available2024-04-04T03:18:32Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194415
dc.description.abstractEnLet $a \in \R,$ and let $k(a)$ be the largest constant such that $sup\vert cos(na)-cos(nb)\vert < k(a)$ for $b\in \R$ implies that $b \in \pm a+2\pi\Z. $ We show thatif a cosine sequence $(C(n))_{n\in \Z}$ with values in a Banach algebra $A$ satisfies $sup_{n\ge 1}\Vert C(n) -cos(na).1_A\Vert < k(a),$ then $C(n)=cos(na)$ for $n\in \Z.$ Since${\sqrt 5\over 2} \le k(a) \le {8\over 3\sqrt 3}$ for every $a \in \R,$ this shows that if some cosine family $(C(g))_{g\in G}$ over an abelian group $G$ in a Banach algebra satisfies $sup_{g\in G}\Vert C(g)-c(g)\Vert < {\sqrt 5\over 2}$ for some scalar cosine family $(c(g))_{g\in G},$ then $C(g)=c(g)$ for $g\in G,$ and the constant ${\sqrt 5\over 2}$ is optimal. We also describe the set of all real numbers $a \in [0,\pi]$ satisfying $k(a)\le {3\over 2}.$
dc.language.isoen
dc.subject.encosine sequence
dc.subject.encosine family
dc.subject.encyclotomic polynomial
dc.subject.enKronecker's theorem
dc.title.enA zero-sqrt(5)/ 2 law for cosine families
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.identifier.arxiv1505.06064
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-01147792
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01147792v1
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.au=ESTERLE,%20Jean&amp;rft.genre=preprint


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