Multipliers of Dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables

[EN] Let H-infinity be the set of all ordinary Dirichlet series D = Sigma(n) a(n)(n-1) ann-s representing bounded holomorphic functions on the right half plane. A completely multiplicative sequence (b(n)) of complex numbers is said to be an l(1)-multiplier for H-infinity whenever Sigma(n vertical bar)a(n)b(n vertical bar) < infinity for every D is an element of H-infinity. We study the problem of describing such sequences (b(n)) in terms of the asymptotic decay of the subsequence (b(pj)), where p(j) denotes the j th prime number. Given a completely multiplicative sequence b = (b(n)) we prove (among other results): b is an l(1)-multiplier for H-infinity provided vertical bar b(pj)vertical bar < 1 for all j and (lim(n)) over bar 1/log(n) Sigma(n)(j=1) b(p j)*(2) < 1, and conversely, if b is an l(1)-multiplier for H-infinity, then vertical bar b(pj)vertical bar < 1 for all j and (lim(n)) over bar 1/log(n) Sigma(n)(j=1) b(p j)*(2) <= 1 (here b* stands for the decreasing rearrangement of b). Following an ingenious idea of Harald Bohr it turns out that this problem is intimately related with the question of characterizing those sequences z in the infinite dimensional polydisk D-infinity (the open unit ball of l(infinity)) for which every bounded and holomorphic function f on D-infinity has an absolutely convergent monomial series expansion Sigma(alpha) partial derivative alpha f (0)/alpha! z alpha. Moreover, we study analogous problems in Hardy spaces of Dirichlet series and Hardy spaces of functions on the infinite dimensional polytorus T-infinity.The second, fourth and fifth authors were supported by MINECO and FEDER Project MTM2014-57838-C2-2-P. The fourth author was also supported by PrometeoII/2013/013. The fifth author was also supported by project SP-UPV20120700.Bayart, F.; Defant, A.; Frerick, L.; Maestre, M.; Sevilla Peris, P. (2017). Multipliers of Dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables. Mathematische Annalen. 368(1-2):837-876. https://doi.org/10.1007/s00208-016-1511-1S8378763681-2Aleman, A., Olsen, J.-F., Saksman, E.: Fatou and brother Riesz theorems in the infinite-dimensional polydisc. arXiv:1512.01509Balasubramanian, R., Calado, B., Queffélec, H.: The Bohr inequality for ordinary Dirichlet series. 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Harpgophytum procumbens for osteoarthritis and low back pain: A systematic review

BACKGROUND: The objective of this review is to determine the effectiveness of Harpagophytum procumbens preparations in the treatment of various forms of musculoskeletal pain. METHODS: Several databases and other sources were searched to identify randomized controlled trials, quasi-randomized controlled trials, and controlled clinical trials testing Harpagophytum preparations in adults suffering from pain due to osteoarthritis or low back pain. RESULTS: Given the clinical heterogeneity and insufficient data for statistical pooling, trials were described in a narrative way, taking into consideration methodological quality scores. Twelve trials were included with six investigating osteoarthritis (two were identical trials), four low back pain, and three mixed-pain conditions. CONCLUSIONS: There is limited evidence for an ethanolic Harpagophytum extract containing less than <30 mg harpagoside per day in the treatment of knee and hip osteoarthritis. There is moderate evidence of effectiveness for (1) the use of a Harpagophytum powder at 60 mg harpagoside in the treatment of osteoarthritis of the spine, hip and knee; (2) the use of an aqueous Harpagophytum extract at a daily dose of 100 mg harpagoside in the treatment of acute exacerbations of chronic non-specific low back pain; and (3) the use of an aqueous extract of Harpagophytum procumbens at 60 mg harpagoside being non-inferior to 12.5 mg rofecoxib per day for chronic non-specific low-back pain (NSLBP) in the short term. Strong evidence exists for the use of an aqueous Harpagophytum extract at a daily dose equivalent of 50 mg harpagoside in the treatment of acute exacerbations of chronic NSLBP

Distributionally chaotic families of operators on Fréchet spaces

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Communications on Pure and Applied Analysis (CPAA) following peer review. The definitive publisher-authenticated version Conejero, J. A., Kostić, M., Miana, P. J., & Murillo-Arcila, M. (2016). Distributionally chaotic families of operators on Fréchet spaces.Communications on Pure and Applied Analysis, 2016, vol. 15, no 5, p. 1915-1939, is available online at: http://dx.doi.org/10.3934/cpaa.2016022The existence of distributional chaos and distributional irregular vectors has been recently considered in the study of linear dynamics of operators and C-0-semigroups. In this paper we extend some previous results on both notions to sequences of operators, C-0-semigroups, C-regularized semigroups, and alpha-timesintegrated semigroups on Frechet spaces. We also add a study of rescaled distributionally chaotic C-0-semigroups. Some examples are provided to illustrate all these results.The first and fourth authors are supported in part by MEC Project MTM2010-14909, MTM2013-47093-P, and Programa de Investigacion y Desarrollo de la UPV, Ref. SP20120700. The second author is partially supported by grant 174024 of Ministry of Science and Technological Development, Republic of Serbia. The third author has been partially supported by Project MTM2013-42105-P, DGI-FEDER, of the MCYTS; Project E-64, D.G. Aragon, and Project UZCUD2014-CIE-09, Universidad de Zaragoza. The fourth author is supported by a grant of the FPU Program of Ministry of education of Spain.Conejero, JA.; Kostic, M.; Miana Sanz, PJ.; Murillo Arcila, M. (2016). Distributionally chaotic families of operators on Fréchet spaces. Communications on Pure and Applied Analysis. 15(5):1915-1939. https://doi.org/10.3934/cpaa.2016022S1915193915

A systematic review on the effectiveness of complementary and alternative medicine for chronic non-specific low-back pain

The purpose of this systematic review was to assess the effects of spinal manipulative therapy (SMT), acupuncture and herbal medicine for chronic non-specific LBP. A comprehensive search was conducted by an experienced librarian from the Cochrane Back Review Group (CBRG) in multiple databases up to December 22, 2008. Randomised controlled trials (RCTs) of adults with chronic non-specific LBP, which evaluated at least one clinically relevant, patient-centred outcome measure were included. Two authors working independently from one another assessed the risk of bias using the criteria recommended by the CBRG and extracted the data. The data were pooled when clinically homogeneous and statistically possible or were otherwise qualitatively described. GRADE was used to determine the quality of the evidence. In total, 35 RCTs (8 SMT, 20 acupuncture, 7 herbal medicine), which examined 8,298 patients, fulfilled the inclusion criteria. Approximately half of these (2 SMT, 8 acupuncture, 7 herbal medicine) were thought to have a low risk of bias. In general, the pooled effects for the studied interventions demonstrated short-term relief or improvement only. The lack of studies with a low-risk of bias, especially in regard to SMT precludes any strong conclusions; however, the principal findings, which are based upon low- to very-low-quality evidence, suggest that SMT does not provide a more clinically beneficial effect compared with sham, passive modalities or any other intervention for treatment of chronic low-back pain. There is evidence, however, that acupuncture provides a short-term clinically relevant effect when compared with a waiting list control or when acupuncture is added to another intervention. Although there are some good results for individual herbal medicines in short-term individual trials, the lack of homogeneity across studies did not allow for a pooled estimate of the effect. In general, these results are in agreement with other recent systematic reviews on SMT, but in contrast with others. These results are also in agreement with recent reviews on acupuncture and herbal medicine. Randomized trials with a low risk of bias and adequate sample sizes are direly needed