The Cesàro operator in growth Banach spaces of analytic functions

[EN] The CesA ro operator C, when acting in the classical growth Banach spaces and , for , of analytic functions on , is investigated. Based on a detailed knowledge of their spectra (due to A. Aleman and A.-M. Persson) we are able to determine the norms of these operators precisely. It is then possible to characterize the mean ergodic and related properties of C acting in these spaces. In addition, we determine the largest Banach space of analytic functions on which C maps into (resp. into ); this optimal domain space always contains (resp. ) as a proper subspace.The research of the first two authors was partially supported by the projects MTM2013-43540-P and GVA Prometeo II/2013/013.Albanese, A.; Bonet Solves, JA.; Ricker, WJ. (2016). The Cesàro operator in growth Banach spaces of analytic functions. Integral Equations and Operator Theory. 86(1):97-112. https://doi.org/10.1007/s00020-016-2316-zS97112861Albanese A.A., Bonet J., Ricker W.J.: Convergence of arithmetic means of operators in Fréchet spaces. J. Math. Anal. Appl. 401, 160–173 (2013)Albanese, A.A., Bonet, J.,Ricker, W.J.: The Cesàro operator on power series spaces. Preprint (2016)Albrecht E., Miller T.L., Neumann M.M.: Spectral properties of generalized Cesàro operators on Hardy and weighted Bergman spaces. Archiv Math. 85, 446–459 (2005)Aleman A.: A class of integral operators on spaces of analytic functions. In: Proc. of the Winter School in Operator Theory and Complex Analysis, Univ. Málaga Secr. Publ., Málaga, pp. 3–30 (2007)Aleman A., Constantin O.: Spectra of integration operators on weighted Bergman spaces. J. Anal. Math. 109, 199–231 (2009)Aleman A., Persson A.-M.: Resolvent estimates and decomposable extensions of generalized Cesàro operators. J. Funct. Anal. 258, 67–98 (2010)Aleman A., Siskakis A.G.: An integral operator on H p . Complex Var. Theory Appl. 28, 149–158 (1995)Aleman A., Siskakis A.G.: Integration operators on Bergman spaces. Indiana Univ. Math. J. 46, 337–356 (1997)Bayart F., Matheron E.: Dynamics of Linear Operators. Cambridge University Press, Cambridge (2009)Bierstedt K.D., Bonet J., Galbis A.: Weighted spaces of holomorphic functions on balanced domains. Michigan Math. J. 40, 271–297 (1993)Bierstedt K.D., Bonet J., Taskinen J.: Associated weights and spaces of holomorphic functions. Studia Math. 127, 137–168 (1998)Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Aust. Math. Soc. 54, 70–79 (1993)Bonet J., Domanski P., Lindström M.: Essential norm and weak compactness on weighted Banach spaces of analytic functions. Can. Math. Bull. 42, 139–148 (1999)Curbera G.P., Ricker W.J.: Extensions of the classical Cesàro operator on Hardy spaces. Math. Scand. 108, 279–290 (2011)Danikas N., Siskakis A.: The Cesàro operator on bounded analytic functions. Analysis 13, 295–299 (1993)Duren P.: Theory of H p Spaces. Academic Press, New York (1970)Dunford N., Schwartz J.T.:Linear Operators I: General Theory, 2nd Printing. Wiley Interscience Publ., New York (1964)Grosse-Erdmann K., Peris A.: Linear Chaos. Springer, London (2011)Harutyunyan A., Lusky W.: On the boundedness of the differentiation operator between weighted spaces of holomorphic functions. Studia Math. 184, 233–247 (2008)Hedenmalm H., Korenblum B., Zhu K.: Theory of Bergman Spaces. Grad. Texts in Math., vol. 199. Springer, New York (2000)Katzelson Y., Tzafriri L.: On power bounded operators. J. Funct. Anal. 68, 313–328 (1968)Krengel U.: Ergodic Theorems. de Gruyter Studies in Mathematics, vol. 6. Walter de Gruyter Co., Berlin (1985)Lin M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 337–340 (1974)Lusky W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Studia Math. 175(1), 19–40 (2006)Megginson R.E.: An Introduction to Banach Space Theory. Springer, New York (1998)Meise R., Vogt D.: Introduction to Functional Analysis. Clarendon Press, Oxford (1997)Persson A.-M.: On the spectrum of the Cesàro operator on spaces of analytic functions. J. Math. Anal. Appl. 340, 1180–1203 (2008)Rubel L.A., Shields A.L.: The second dual of certain spaces of analytic functions. J. Aust. Math. Soc. 11, 276–280 (1970)Shields A.L., Williams D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Am. Math. Soc. 162, 287–302 (1971)Siskakis A.: Volterra operators on spaces of analytic functions—a survey. In: Proc. of the First Advanced Course in Operator Theory and Complex Analysis, Univ. Sevilla Serc. Publ., Seville, pp. 51–68 (2006

Herschel Planetary Nebula Survey (HerPlaNS) - First Detection of OH+ in Planetary Nebulae

We report the first detections of OH$^+$ emission in planetary nebulae (PNe). As part of an imaging and spectroscopy survey of 11 PNe in the far-IR using the PACS and SPIRE instruments aboard the Herschel Space Observatory, we performed a line survey in these PNe over the entire spectral range between 51 and 672$\mu$m to look for new detections. OH$^+$ rotational emission lines at 152.99, 290.20, 308.48, and 329.77$\mu$m were detected in the spectra of three planetary nebulae: NGC 6445, NGC 6720, and NGC 6781. Excitation temperatures and column densities derived from these lines are in the range of 27 to 47 K and 2$\times$10$^{10}$ to 4 $\times$10$^{11}$ cm$^{-2}$, respectively. In PNe, the OH+ rotational line emission appears to be produced in the photodissociation region (PDR) in these objects. The emission of OH+ is observed only in PNe with hot central stars (T$_{eff}$ > 100000 K), suggesting that high-energy photons may play a role in the OH+ formation and its line excitation in these objects, as it seems to be the case for ultraluminous galaxies.Comment: 9 pages, 7 figures; accepted for publication in A&

A Statistical Inference Method for Interpreting the CLASP Observations

On 3rd September 2015, the Chromospheric Lyman-Alpha SpectroPolarimeter (CLASP) successfully measured the linear polarization produced by scattering processes in the hydrogen Lyman-$\alpha$ line of the solar disk radiation, revealing conspicuous spatial variations in the $Q/I$ and $U/I$ signals. Via the Hanle effect the line-center $Q/I$ and $U/I$ amplitudes encode information on the magnetic field of the chromosphere-corona transition region (TR), but they are also sensitive to the three-dimensional structure of this corrugated interface region. With the help of a simple line formation model, here we propose a statistical inference method for interpreting the Lyman-$\alpha$ line-center polarization observed by CLASP.Comment: Accepted for publication in The Astrophysical Journa

Perturbative evolution of particle orbits around Kerr black holes: time domain calculation

Treating the Teukolsky perturbation equation numerically as a 2+1 PDE and smearing the singularities in the particle source term by the use of narrow Gaussian distributions, we have been able to reproduce earlier results for equatorial circular orbits that were computed using the frequency domain formalism. A time domain prescription for a more general evolution of nearly geodesic orbits under the effects of radiation reaction is presented. This approach can be useful when tackling the more realistic problem of a stellar-mass black hole moving on a generic orbit around a supermassive black hole under the influence of radiation reaction forces.Comment: 8 pages, 5 figures, problems with references and double-printing fixe

Extreme Mass Ratio Inspirals: LISA's unique probe of black hole gravity

In this review article I attempt to summarise past and present-ongoing-work on the problem of the inspiral of a small body in the gravitational field of a much more massive Kerr black hole. Such extreme mass ratio systems, expected to occur in galactic nuclei, will constitute prime sources of gravitational radiation for the future LISA gravitational radiation detector. The article's main goal is to provide a survey of basic celestial mechanics in Kerr spacetime and calculations of gravitational waveforms and backreaction on the small body's orbital motion, based on the traditional `flux-balance' method and the Teukolsky black hole perturbation formalism.Comment: Invited review article, 45 pages, 23 figure

Involving young people in health promotion, research and policy-making : practical recommendations

Youth is a dynamic and complex transition period in life where many factors jeopardize its present and future health. Youth involvement enables young people to influence processes and decisions that affect them, leading to changes in themselves and their environment (e.g. peers, services, communities and policies); this strategy could be applied to improve health and prevent diseases. Nonetheless, scientific evidence of involving youth in health-related programmes is scarce. The aim of this paper is to describe youth involvement as a health promotion strategy and to compile practical recommendations for health promoters, researchers and policy makers interested in successful involvement of young people in health-related programmes. These suggestions aim to encourage a positive working synergy between adults and youth during the development, implementation and evaluation of policies, research and/or health promotion efforts that target adolescents.PostprintPeer reviewe

IMRT beam angle optimization using electromagnetism-like algorithm

The selection of appropriate beam irradiation directions in radiotherapy – beam angle optimization (BAO) problem – is very impor- tant for the quality of the treatment, both for improving tumor irradia- tion and for better organs sparing. However, the BAO problem is still not solved satisfactorily and, most of the time, beam directions continue to be manually selected in clinical practice which requires many trial and error iterations between selecting beam angles and computing fluence patterns until a suitable treatment is achieved. The objective of this pa- per is to introduce a new approach for the resolution of the BAO problem, using an hybrid electromagnetism-like algorithm with descent search to tackle this highly non-convex optimization problem. Electromagnetism- like algorithms are derivative-free optimization methods with the ability to avoid local entrapment. Moreover, the hybrid electromagnetism-like algorithm with descent search has a high ability of producing descent directions. A set of retrospective treated cases of head-and-neck tumors at the Portuguese Institute of Oncology of Coimbra is used to discuss the benefits of the proposed algorithm for the optimization of the BAO problem.Fundação para a Ciência e a Tecnologia (FCT

Widespread sex differences in gene expression and splicing in the adult human brain

There is strong evidence to show that men and women differ in terms of neurodevelopment, neurochemistry and susceptibility to neurodegenerative and neuropsychiatric disease. The molecular basis of these differences remains unclear. Progress in this field has been hampered by the lack of genome-wide information on sex differences in gene expression and in particular splicing in the human brain. Here we address this issue by using post-mortem adult human brain and spinal cord samples originating from 137 neuropathologically confirmed control individuals to study whole-genome gene expression and splicing in 12 CNS regions. We show that sex differences in gene expression and splicing are widespread in adult human brain, being detectable in all major brain regions and involving 2.5% of all expressed genes. We give examples of genes where sex-biased expression is both disease-relevant and likely to have functional consequences, and provide evidence suggesting that sex biases in expression may reflect sex-biased gene regulatory structures

The Herschel Planetary Nebula Survey (HerPlaNS) I. Data Overview and Analysis Demonstration with NGC 6781

This is the first of a series of investigations into far-IR characteristics of 11 planetary nebulae (PNs) under the Herschel Space Observatory Open Time 1 program, Herschel Planetary Nebula Survey (HerPlaNS). Using the HerPlaNS data set, we look into the PN energetics and variations of the physical conditions within the target nebulae. In the present work, we provide an overview of the survey, data acquisition and processing, and resulting data products. We perform (1) PACS/SPIRE broadband imaging to determine the spatial distribution of the cold dust component in the target PNs and (2) PACS/SPIRE spectral-energy-distribution (SED) and line spectroscopy to determine the spatial distribution of the gas component in the target PNs. For the case of NGC 6781, the broadband maps confirm the nearly pole-on barrel structure of the amorphous carbon-richdust shell and the surrounding halo having temperatures of 26-40 K. The PACS/SPIRE multi-position spectra show spatial variations of far-IR lines that reflect the physical stratification of the nebula. We demonstrate that spatially-resolved far-IR line diagnostics yield the (T_e, n_e) profiles, from which distributions of ionized, atomic, and molecular gases can be determined. Direct comparison of the dust and gas column mass maps constrained by the HerPlaNS data allows to construct an empirical gas-to-dust mass ratio map, which shows a range of ratios with the median of 195+-110. The present analysis yields estimates of the total mass of the shell to be 0.86 M_sun, consisting of 0.54 M_sun of ionized gas, 0.12 M_sun of atomic gas, 0.2 M_sun of molecular gas, and 4 x 10^-3 M_sun of dust grains. These estimates also suggest that the central star of about 1.5 M_sun initial mass is terminating its PN evolution onto the white dwarf cooling track.Comment: 27 pages, 16 figures, accepted for publication in A&

Development and characterization of the readout system for POLARBEAR-2

POLARBEAR-2 is a next-generation receiver for precision measurements of the polarization of the cosmic microwave background (Cosmic Microwave Background (CMB)). Scheduled to deploy in early 2015, it will observe alongside the existing POLARBEAR-1 receiver, on a new telescope in the Simons Array on Cerro Toco in the Atacama desert of Chile. For increased sensitivity, it will feature a larger area focal plane, with a total of 7,588 polarization sensitive antenna-coupled Transition Edge Sensor (TES) bolometers, with a design sensitivity of 4.1 uKrt(s). The focal plane will be cooled to 250 milliKelvin, and the bolometers will be read-out with 40x frequency domain multiplexing, with 36 optical bolometers on a single SQUID amplifier, along with 2 dark bolometers and 2 calibration resistors. To increase the multiplexing factor from 8x for POLARBEAR-1 to 40x for POLARBEAR-2 requires additional bandwidth for SQUID readout and well-defined frequency channel spacing. Extending to these higher frequencies requires new components and design for the LC filters which define channel spacing. The LC filters are cold resonant circuits with an inductor and capacitor in series with each bolometer, and stray inductance in the wiring and equivalent series resistance from the capacitors can affect bolometer operation. We present results from characterizing these new readout components. Integration of the readout system is being done first on a small scale, to ensure that the readout system does not affect bolometer sensitivity or stability, and to validate the overall system before expansion into the full receiver. We present the status of readout integration, and the initial results and status of components for the full array.Comment: Presented at SPIE Astronomical Telescopes and Instrumentation 2014: Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy VII. Published in Proceedings of SPIE Volume 915