212 research outputs found
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 and . 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 . 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 . 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 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 . 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
Landscape Diversity Related to Buruli Ulcer Disease in Côte d'Ivoire
Buruli ulcer (BU) is one of the most neglected but treatable tropical diseases. The causative organism, Mycobacterium ulcerans, is from the family of bacteria that causes tuberculosis and leprosy. This severe skin disease leads to long-term functional disability if not treated. BU has been reported in over 30 countries mainly with tropical and subtropical climates, but Côte d'Ivoire is one of the most affected countries. M. ulcerans is an environmental bacterium and its mode of transmission to humans is still unclear, such that the disease is often referred to as the “mysterious disease” or the “new leprosy”. Here, we explored the relationship between environmental and socioeconomic factors and BU cases on a nationwide scale. We found that irrigated rice field cultures areas, and, to a lesser extent, banana fields as well as areas in the vicinity of dams used for irrigation and aquaculture purposes, represent high risk zones for the human population to contract BU in Côte d'Ivoire. This work identifies high-risk areas for BU in Côte d'Ivoire and deserves to be extended to different countries. We need now to obtain a global vision and understanding of the route of transmission of M. ulcerans to humans in order to better implement control strategies
The Manipulative Complexity of Lower Paleolithic Stone Toolmaking
Early stone tools provide direct evidence of human cognitive and behavioral evolution that is otherwise unavailable. Proper interpretation of these data requires a robust interpretive framework linking archaeological evidence to specific behavioral and cognitive actions.Here we employ a data glove to record manual joint angles in a modern experimental toolmaker (the 4(th) author) replicating ancient tool forms in order to characterize and compare the manipulative complexity of two major Lower Paleolithic technologies (Oldowan and Acheulean). To this end we used a principled and general measure of behavioral complexity based on the statistics of joint movements.This allowed us to confirm that previously observed differences in brain activation associated with Oldowan versus Acheulean technologies reflect higher-level behavior organization rather than lower-level differences in manipulative complexity. This conclusion is consistent with a scenario in which the earliest stages of human technological evolution depended on novel perceptual-motor capacities (such as the control of joint stiffness) whereas later developments increasingly relied on enhanced mechanisms for cognitive control. This further suggests possible links between toolmaking and language evolution
Forcing Versus Feedback: Epidemic Malaria and Monsoon Rains in Northwest India
Malaria epidemics in regions with seasonal windows of transmission can vary greatly in size from year to year. A central question has been whether these interannual cycles are driven by climate, are instead generated by the intrinsic dynamics of the disease, or result from the resonance of these two mechanisms. This corresponds to the more general inverse problem of identifying the respective roles of external forcings vs. internal feedbacks from time series for nonlinear and noisy systems. We propose here a quantitative approach to formally compare rival hypotheses on climate vs. disease dynamics, or external forcings vs. internal feedbacks, that combines dynamical models with recently developed, computational inference methods. The interannual patterns of epidemic malaria are investigated here for desert regions of northwest India, with extensive epidemiological records for Plasmodium falciparum malaria for the past two decades. We formulate a dynamical model of malaria transmission that explicitly incorporates rainfall, and we rely on recent advances on parameter estimation for nonlinear and stochastic dynamical systems based on sequential Monte Carlo methods. Results show a significant effect of rainfall in the inter-annual variability of epidemic malaria that involves a threshold in the disease response. The model exhibits high prediction skill for yearly cases in the malaria transmission season following the monsoonal rains. Consideration of a more complex model with clinical immunity demonstrates the robustness of the findings and suggests a role of infected individuals that lack clinical symptoms as a reservoir for transmission. Our results indicate that the nonlinear dynamics of the disease itself play a role at the seasonal, but not the interannual, time scales. They illustrate the feasibility of forecasting malaria epidemics in desert and semi-arid regions of India based on climate variability. This approach should be applicable to malaria in other locations, to other infectious diseases, and to other nonlinear systems under forcing
Attentional Set-Shifting Deficit in Parkinson’s Disease Is Associated with Prefrontal Dysfunction: An FDG-PET Study
The attentional set-shifting deficit that has been observed in Parkinson’s disease (PD) has long been considered neuropsychological evidence of the involvement of meso-prefrontal and prefrontal-striatal circuits in cognitive flexibility. However, recent studies have suggested that non-dopaminergic, posterior cortical pathologies may also contribute to this deficit. Although several neuroimaging studies have addressed this issue, the results of these studies were confounded by the use of tasks that required other cognitive processes in addition to set-shifting, such as rule learning and working memory. In this study, we attempted to identify the neural correlates of the attentional set-shifting deficit in PD using a compound letter task and 18F-fluoro-deoxy-glucose (FDG) positron emission tomography during rest. Shift cost, which is a measure of attentional set-shifting ability, was significantly correlated with hypometabolism in the right dorsolateral prefrontal cortex, including the putative human frontal eye field. Our results provide direct evidence that dysfunction in the dorsolateral prefrontal cortex makes a primary contribution to the attentional set-shifting deficit that has been observed in PD patients
Dissociable effects of noradrenaline, dopamine, and serotonin uptake blockade on stop task performance in rats
On the improvement of inhibitory response control and visuospatial attention by indirect and direct adrenoceptor agonists
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