There exist multilinear Bohnenblust-Hille constants (Cn)n=1(infinity) with limn ->infinity(Cn+1-Cn)=0
| dc.contributor.author | Nuñez Alarcón, D. | |
| dc.contributor.author | Pellegrino, Daniel | |
| dc.contributor.author | Seoane-Sepúlveda, Juan B. | |
| dc.contributor.author | Serrano Rodríguez, D.M. | |
| dc.date.accessioned | 2023-06-20T00:25:21Z | |
| dc.date.available | 2023-06-20T00:25:21Z | |
| dc.date.issued | 2013 | |
| dc.description.abstract | The n-linear Bohnenblust-Hille inequality asserts that there is a constant C-n is an element of [1, infinity) such that the l(2n/n+1)-norm of (U(e(i1), ..., e(in)))(i1, ...,in=1)(N) is bounded above by C-n times the supremum norm of U, for any n-linear form U :C-N x ... x C-N -> C and N is an element of N (the same holds for real scalars). We prove what we call Fundamental Lemma, which brings new information on the optimal constants, (K-n)(n=1)(infinity) for both real and complex scalars. For instance, Kn+1 - K-n < 0.87/n(0.473) for infinitely many n's. For complex scalars we give a formula (of surprisingly low growth), in which pi, e and the famous Euler-Mascheroni constant gamma appear: K-n < 1 (4/root pi (1 - e(gamma/2-1/2)) Sigma(n-1)(j=1) j(log2(e-gamma/2+1/2)-1)), for all(n) >= 2. We study the interplay between the Kahane-Salem-Zygmund and the Bohnenblust-Hille (polynomial and multilinear) inequalities and provide estimates for Bohnenblust-Hille-type inequality constants for any exponent q is an element of [2n/n+1, infinity). (C) 2012 Elsevier Inc. All rights reserved. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Capes. | |
| dc.description.sponsorship | CNPq | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/19923 | |
| dc.identifier.doi | 10.1016/j.jfa.2012.11.006 | |
| dc.identifier.issn | 0022-1236 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0022123612004156 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com | |
| dc.identifier.relatedurl | http://arxiv.org/pdf/1207.0124.pdf | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/42545 | |
| dc.issue.number | 2 | |
| dc.journal.title | Journal of Functional Analysis | |
| dc.language.iso | eng | |
| dc.page.final | 463 | |
| dc.page.initial | 429 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | Grants 301237/2009-3 | |
| dc.relation.projectID | 477124/2012-7. | |
| dc.relation.projectID | MTM2009-07848. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 530.1 | |
| dc.subject.keyword | Bohnenblust-Hille inequality | |
| dc.subject.keyword | Kahane-Salem-Zygmund inequality | |
| dc.subject.keyword | Quantum Information Theory | |
| dc.subject.ucm | Física matemática | |
| dc.title | There exist multilinear Bohnenblust-Hille constants (Cn)n=1(infinity) with limn ->infinity(Cn+1-Cn)=0 | |
| dc.type | journal article | |
| dc.volume.number | 264 | |
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| dspace.entity.type | Publication |
