Weighted composition operators on Korenblum type spaces of analytic functions

[EN] We investigate the continuity, compactness and invertibility of weighted composition operators W-psi,W-phi: f -> psi(f circle phi) when they act on the classical Korenblum space A(-infinity) and other related Frechet or (LB)-spaces of analytic functions on the open unit disc which are defined as intersections or unions of weighted Banach spaces with sup-norms. Some results about the spectrum of these operators are presented in case the self-map phi has a fixed point in the unit disc. A precise description of the spectrum is obtained in this case when the operator acts on the Korenblum space.This research was partially supported by the research project MTM2016-76647-P and the grant BES-2017-081200.Gomez-Orts, E. (2020). Weighted composition operators on Korenblum type spaces of analytic functions. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(4):1-15. https://doi.org/10.1007/s13398-020-00924-1S1151144Abramovich, Y.A., Aliprantis, C.D.: An invitation to operator theory. Graduate Studies in Mathematics. Amer. Math. Soc., 50 (2002)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in the Fréchet spaces $$\ell ^{p+}$$ and $$L^{p-}$$. Glasgow Math. J. 59, 273–287 (2017)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator on Korenblum type spaces of analytic functions. Collect. Math. 69(2), 263–281 (2018)Albanese, A.A., Bonet, J., Ricker, W.J.: Operators on the Fréchet sequence spaces $$ces(p+), 1\le p\le \infty$$. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(2), 1533–1556 (2019)Albanese, A.A., Bonet, J., Ricker, W.J.: Linear operators on the (LB)-sequence spaces $$ces(p-), 1\le p\le \infty$$. Descriptive topology and functional analysis. II, 43–67, Springer Proc. Math. Stat., 286, Springer, Cham (2019)Arendt, W., Chalendar, I., Kumar, M., Srivastava, S.: Powers of composition operators: asymptotic behaviour on Bergman, Dirichlet and Bloch spaces. J. Austral. Math. Soc. 1–32. https://doi.org/10.1017/S1446788719000235Aron, R., Lindström, M.: Spectra of weighted composition operators on weighted Banach spaces of analytic funcions. Israel J. Math. 141, 263–276 (2004)Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Austral. Math. Soc., Ser. A, 54(1), 70–79 (1993)Bonet, J.: A note about the spectrum of composition operators induced by a rotation. RACSAM 114, 63 (2020). https://doi.org/10.1007/s13398-020-00788-5Bonet, J., Domański, P., Lindström, M., Taskinen, J.: Composition operators between weighted Banach spaces of analytic functions. J. Austral. Math. Soc., Ser. A, 64(1), 101–118 (1998)Bourdon, P.S.: Essential angular derivatives and maximum growth of Königs eigenfunctions. J. Func. Anal. 160, 561–580 (1998)Bourdon, P.S.: Invertible weighted composition operators. Proc. Am. Math. Soc. 142(1), 289–299 (2014)Carleson, L., Gamelin, T.: Complex Dynamics. Springer, Berlin (1991)Cowen, C., MacCluer, B.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton, FL (1995)Contreras, M., Hernández-Díaz, A.G.: Weighted composition operators in weighted Banach spacs of analytic functions. J. Austral. Math. Soc., Ser. A 69, 41–60 (2000)Eklund, T., Galindo, P., Lindström, M.: Königs eigenfunction for composition operators on Bloch and $$H^\infty$$ spaces. J. Math. Anal. Appl. 445, 1300–1309 (2017)Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Grad. Texts in Math. 199. Springer, New York (2000)Jarchow, H.: Locally Convex Spaces. Teubner, Stuttgart (1981)Kamowitz, H.: Compact operators of the form $$uC_{\varphi }$$. Pac. J. Math. 80(1) (1979)Korenblum, B.: An extension of the Nevanlinna theory. Acta Math. 135, 187–219 (1975)Köthe, G.: Topological Vector Spaces II. Springer, New York Inc (1979)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomophic functions. Stud. Math. 75, 19–45 (2006)Meise, R., Vogt, D.: Introduction to functional analysis. Oxford Grad. Texts in Math. 2, New York, (1997)Montes-Rodríguez, A.: Weighted composition operators on weighted Banach spaces of analytic functions. J. Lond. Math. Soc. 61(3), 872–884 (2000)Queffélec, H., Queffélec, M.: Diophantine Approximation and Dirichlet series. Hindustain Book Agency, New Delhi (2013)Shapiro, J.H.: Composition Operators and Classical Function Theory. Springer, New York (1993)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Amer. Math. Soc. 162, 287–302 (1971)Zhu, K.: Operator Theory on Function Spaces, Math. Surveys and Monographs, Amer. Math. Soc. 138 (2007

Use of antidepressant medications in relation to the incidence of breast cancer

Although associations have been reported between antidepressant use and risk of breast cancer, the findings have been inconsistent. We conducted a population-based case–control study among women enrolled in Group Health Cooperative (GHC), a health maintenance organization in Washington State. Women with a first primary breast cancer diagnosed between 1990 and 2001 were identified (N=2904) and five controls were selected for each case (N=14396). Information on antidepressant use was ascertained through the GHC pharmacy database and on breast cancer risk factors and screening mammograms from GHC records. Prior to one year before diagnosis of breast cancer, about 20% of cases and controls had used tricyclic antidepressants (adjusted odds ratio=1.06, 95% CI 0.94–1.19) and 6% of each group had used selective serotonin reuptake inhibitors (OR=0.98, 95% CI 0.80–1.18). There also were no differences between cases and controls with regard to the number of prescriptions filled or the timing of use. Taken as a whole, the results from this and other studies to date do not indicate an altered risk of breast cancer associated with the use of antidepressants overall, by class, or for individual antidepressants

Interaction between Coastal and Oceanic Ecosystems of the Western and Central Pacific Ocean through Predator-Prey Relationship Studies

The Western and Central Pacific Ocean sustains the highest tuna production in the world. This province is also characterized by many islands and a complex bathymetry that induces specific current circulation patterns with the potential to create a high degree of interaction between coastal and oceanic ecosystems. Based on a large dataset of oceanic predator stomach contents, our study used generalized linear models to explore the coastal-oceanic system interaction by analyzing predator-prey relationship. We show that reef organisms are a frequent prey of oceanic predators. Predator species such as albacore (Thunnus alalunga) and yellowfin tuna (Thunnus albacares) frequently consume reef prey with higher probability of consumption closer to land and in the western part of the Pacific Ocean. For surface-caught-predators consuming reef prey, this prey type represents about one third of the diet of predators smaller than 50 cm. The proportion decreases with increasing fish size. For predators caught at depth and consuming reef prey, the proportion varies with predator species but generally represents less than 10%. The annual consumption of reef prey by the yellowfin tuna population was estimated at 0.8±0.40CV million tonnes or 2.17×1012±0.40CV individuals. This represents 6.1%±0.17CV in weight of their diet. Our analyses identify some of the patterns of coastal-oceanic ecosystem interactions at a large scale and provides an estimate of annual consumption of reef prey by oceanic predators

Networks and social capital: a relational approach to primary healthcare reform

Collaboration among health care providers and across systems is proposed as a strategy to improve health care delivery the world over. Over the past two decades, health care providers have been encouraged to work in partnership and build interdisciplinary teams. More recently, the notion of networks has entered this discourse but the lack of consensus and understanding about what is meant by adopting a network approach in health services limits its use. Also crucial to this discussion is the work of distinguishing the nature and extent of the impact of social relationships – generally referred to as social capital. In this paper, we review the rationale for collaboration in health care systems; provide an overview and synthesis of key concepts; dispel some common misconceptions of networks; and apply the theory to an example of primary healthcare network reform in Alberta (Canada). Our central thesis is that a relational approach to systems change, one based on a synthesis of network theory and social capital can provide the fodation for a multi-focal approach to primary healthcare reform. Action strategies are recommended to move from an awareness of 'networks' to fully translating knowledge from existing theory to guide planning and practice innovations. Decision-makers are encouraged to consider a multi-focal approach that effectively incorporates a network and social capital approach in planning and evaluating primary healthcare reform

Genetic Structure Among 50 Species of the Northeastern Pacific Rocky Intertidal Community

Comparing many species' population genetic patterns across the same seascape can identify species with different levels of structure, and suggest hypotheses about the processes that cause such variation for species in the same ecosystem. This comparative approach helps focus on geographic barriers and selective or demographic processes that define genetic connectivity on an ecosystem scale, the understanding of which is particularly important for large-scale management efforts. Moreover, a multispecies dataset has great statistical advantages over single-species studies, lending explanatory power in an effort to uncover the mechanisms driving population structure. Here, we analyze a 50-species dataset of Pacific nearshore invertebrates with the aim of discovering the most influential structuring factors along the Pacific coast of North America. We collected cytochrome c oxidase I (COI) mtDNA data from populations of 34 species of marine invertebrates sampled coarsely at four coastal locations in California, Oregon, and Alaska, and added published data from 16 additional species. All nine species with non-pelagic development have strong genetic structure. For the 41 species with pelagic development, 13 show significant genetic differentiation, nine of which show striking FST levels of 0.1–0.6. Finer scale geographic investigations show unexpected regional patterns of genetic change near Cape Mendocino in northern California for five of the six species tested. The region between Oregon and Alaska is a second focus of intraspecific genetic change, showing differentiation in half the species tested. Across regions, strong genetic subdivision occurs more often than expected in mid-to-high intertidal species, a result that may reflect reduced gene flow due to natural selection along coastal environmental gradients. Finally, the results highlight the importance of making primary research accessible to policymakers, as unexpected barriers to marine dispersal break the coast into separate demographic zones that may require their own management plans

High Diversity, Low Disparity and Small Body Size in Plesiosaurs (Reptilia, Sauropterygia) from the Triassic–Jurassic Boundary

Invasion of the open ocean by tetrapods represents a major evolutionary transition that occurred independently in cetaceans, mosasauroids, chelonioids (sea turtles), ichthyosaurs and plesiosaurs. Plesiosaurian reptiles invaded pelagic ocean environments immediately following the Late Triassic extinctions. This diversification is recorded by three intensively-sampled European fossil faunas, spanning 20 million years (Ma). These provide an unparalleled opportunity to document changes in key macroevolutionary parameters associated with secondary adaptation to pelagic life in tetrapods. A comprehensive assessment focuses on the oldest fauna, from the Blue Lias Formation of Street, and nearby localities, in Somerset, UK (Earliest Jurassic: 200 Ma), identifying three new species representing two small-bodied rhomaleosaurids (Stratesaurus taylori gen et sp. nov.; Avalonnectes arturi gen. et sp. nov) and the most basal plesiosauroid, Eoplesiosaurus antiquior gen. et sp. nov. The initial radiation of plesiosaurs was characterised by high, but short-lived, diversity of an archaic clade, Rhomaleosauridae. Representatives of this initial radiation were replaced by derived, neoplesiosaurian plesiosaurs at small-medium body sizes during a more gradual accumulation of morphological disparity. This gradualistic modality suggests that adaptive radiations within tetrapod subclades are not always characterised by the initially high levels of disparity observed in the Paleozoic origins of major metazoan body plans, or in the origin of tetrapods. High rhomaleosaurid diversity immediately following the Triassic-Jurassic boundary supports the gradual model of Late Triassic extinctions, mostly predating the boundary itself. Increase in both maximum and minimum body length early in plesiosaurian history suggests a driven evolutionary trend. However, Maximum-likelihood models suggest only passive expansion into higher body size categories

Genetic Diversity among Enterococcus faecalis

Enterococcus faecalis, a ubiquitous member of mammalian gastrointestinal flora, is a leading cause of nosocomial infections and a growing public health concern. The enterococci responsible for these infections are often resistant to multiple antibiotics and have become notorious for their ability to acquire and disseminate antibiotic resistances. In the current study, we examined genetic relationships among 106 strains of E. faecalis isolated over the past 100 years, including strains identified for their diversity and used historically for serotyping, strains that have been adapted for laboratory use, and isolates from previously described E. faecalis infection outbreaks. This collection also includes isolates first characterized as having novel plasmids, virulence traits, antibiotic resistances, and pathogenicity island (PAI) components. We evaluated variation in factors contributing to pathogenicity, including toxin production, antibiotic resistance, polymorphism in the capsule (cps) operon, pathogenicity island (PAI) gene content, and other accessory factors. This information was correlated with multi-locus sequence typing (MLST) data, which was used to define genetic lineages. Our findings show that virulence and antibiotic resistance traits can be found within many diverse lineages of E. faecalis. However, lineages have emerged that have caused infection outbreaks globally, in which several new antibiotic resistances have entered the species, and in which virulence traits have converged. Comparing genomic hybridization profiles, using a microarray, of strains identified by MLST as spanning the diversity of the species, allowed us to identify the core E. faecalis genome as consisting of an estimated 2057 unique genes

Multi-messenger observations of a binary neutron star merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ~1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of 40+8-8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Mo. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ~40 Mpc) less than 11 hours after the merger by the One- Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ~9 and ~16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta