Landau's necessary density conditions for LCA groups

H. Landau's necessary density conditions for sampling and interpolation may be viewed as a general principle resting on a basic fact of Fourier analysis: The complex exponentials $e^{i kx}$ ($k$ in $\mathbb{Z}$) constitute an orthogonal basis for $L^2([-\pi,\pi])$. The present paper extends Landau's conditions to the setting of locally compact abelian (LCA) groups, relying in an analogous way on the basics of Fourier analysis. The technicalities--in either case of an operator theoretic nature--are however quite different. We will base our proofs on the comparison principle of J. Ramanathan and T. Steger

Weak conditions for interpolation in holomorphic spaces

An analogue of the notion of uniformly separated sequences, expressed in terms of extremal functions, yields a necessary and sufficient condition for interpolation in Lp spaces of holomorphic functions of Paley-Wiener-type when 0 < p \leq 1, of Fock-type when 0 < p \leq 2, and of Bergman-type when 0 < p < \infty. Moreover, if a uniformly discrete sequence has a certain uniform non-uniqueness property with respect to any such Lp space ($0$lt; p &lt; \infty$), then it is an interpolation sequence for that space. The proofs of these results are based on an approximation theorem for subharmonic functions, Beurling's results concerning compactwise limits of sequences, and the description of interpolation sequences in terms of Beurling-type densities. Details are carried out only for Fock spaces, which represent the most difficult case

GCD sums from Poisson integrals and systems of dilated functions

Upper bounds for GCD sums of the form (Formula Presented) are established, where (nk)1≤k≤N is any sequence of distinct positive integers and 0 1/2, a result that in turn settles two longstanding problems on the a.e. behavior of systems of dilated functions: the a.e. growth of sums of the form (Formula Presented)=1 f(nkx) and the a.e. convergence of (Formula Presented)=1 ckf(nkx) when f is 1-periodic and of bounded variation or in Lip1/2. © European Mathematical Society 2015

Reconstruction of Bandlimited Functions from Unsigned Samples

We consider the recovery of real-valued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its Nyquist rate, and may not necessarily be possible if the samples are taken at less than twice the Nyquist rate. In the case of uniform samples, we also describe an FFT-based algorithm to perform the reconstruction. We prove that it converges exponentially rapidly in the number of samples used and examine its numerical behavior on some test cases

Exploring Multimodal Literacy in Language Teaching and Learning

Source at https://myersedpress.presswarehouse.com/browse/book/9781975502133/Data-Analysis-Interpretation-and-Theory-in-Literacy-Studies-Research.In this chapter, we present the research method we used to investigate multimodal literacy in an English-language classroom in a Norwegian lower secondary school. The analytic approach we present combines multimodal analysis with a design-oriented view on learning as a social meaning-making process. The analysis is applied in a smallscale qualitative study of multimodality and literacy in an English as a foreign language (EFL) classroom in Norway. In what follows, we present how we dealt with observations, interviews, and learning materials from work with the novel The Absolutely True Diary of a Part-Time Indian (Alexie, 2007) in a Year 10 classroom. In particular, this chapter aims to demonstrate the process from data to multimodal analysis and go behind the scenes of writing it up. Multimodality serves the double role as an object of study and an analytical approach

Mikrobielle Proteinsynthese im Pansen bei der Verfütterung von artenreichen Grünlandaufwüchsen des Ökologischen Landbaus

Artenreiche und artenarme Grünlandaufwüchse der Jahre 2007 und 2008 wurden hinsichtlich Siliereignung und Futterwert für Wiederkäuer vergleichend untersucht. Die Sommeraufwüchse 2008 wurden siliert und in Stoffwechselversuchen an 4 pansenfistulierte Schafen allein und in Kombination mit Gerste gefüttert. Im Kot wurden die Weender Rohnährstoffe, neutrale (NDF) und saure Detergentienfaser (ADF) sowie N-Fraktionen, im Harn Gesamt-N, Harnstoff, Allantoin und Harnsäure bestimmt. Die mikrobielle Proteinsynthese wurde mittels Dauerinfusionstechnik und Verwendung von 15N als Marker gemessen. Die artenreichen Aufwüchse wiesen hohe Anteile an Leguminosen und Kräutern auf, die artenarmen Aufwüchse bestanden nahezu vollständig aus Gräsern. Der artenarme Frühjahrsaufwuchs 2007 enthielt mehr NDF und ADF als die entsprechende artenreiche Variante. Die Silagen waren reicher an Rohprotein (XP) und Nicht-Faser-Kohlenhydraten zugunsten der artenreichen und enthielten mehr NDF und ADF zugunsten der artenarmen Variante. Die artenreiche Silage wies im Vergleich zur artenarmen Silage höhere Anteile leicht löslicher Inhaltsstoffe und in situ höhere potentielle Trockensubstanz- und NDF-Abbaubarkeiten auf. Bei Fütterung der artenreichen Silage wurden die organische Substanz, XP und ADF höher verdaut, und die Tiere schieden mehr bakteriell gebundenen Kotstickstoff sowie mehr Harnstoff über den Harn als bei Fütterung artenarmer Silage aus. Die Allantoin- und Harnsäureausscheidungen blieben unbeeinflusst von der Silageart. Die artenreiche Silage führte unabhängig von der Fütterung in Kombination mit Gerste zur Steigerung der ruminalen mikrobiellen Proteinsynthese

Some results on the lattice parameters of quaternionic Gabor frames

Gabor frames play a vital role not only modern harmonic analysis but also in several fields of applied mathematics, for instances, detection of chirps, or image processing. In this work we present a non-trivial generalization of Gabor frames to the quaternionic case and give new density results. The key tool is the two-sided windowed quaternionic Fourier transform (WQFT). As in the complex case, we want to write the WQFT as an inner product between a quaternion-valued signal and shifts and modulates of a real-valued window function. We demonstrate a Heisenberg uncertainty principle and for the results regarding the density, we employ the quaternionic Zak transform to obtain necessary and sufficient conditions to ensure that a quaternionic Gabor system is a quaternionic Gabor frame. We conclude with a proof that the Gabor conjecture do not hold true in the quaternionic case

Characterization of individual airborne particles in Taiyuan City, China

Taiyuan, the capital of Shanxi province, China, is one of the most polluted cities in the world. To characterize the ambient particulate pollution, samples of particulates with aerodynamic diameter less than 10 µm (PM(10)) were collected during a 6-day campaign. Individual particles were analyzed by Scanning Electron Microscope with Energy-Dispersive Spectrometer (SEM-EDS) to determine their chemical composition. Meanwhile, photomicrographs were obtained from SEM to aid in particles’ source identification. The lumped data from SEM-EDS were subjected to hierarchical cluster analysis (HCA) to sort out particle types chemically. HCA combined with SEM photomicrographs allowed us to identify 20 different particle types, namely (in order of particle frequency), soil/fly ash particles, coal-burning, sulfur-rich, and iron-rich particles, gypsum, syngenite, quartz, cement, silicon sulfide, siliconferro alloy, calcium-rich particles, ferrochromium alloy, ammonium sulfate and chloride, iron-zinc, ammonium chloride, molybdenum-rich, potassium sulfate, dolomite, lead sulfate, and copper-rich particles. Their possible origins and pathways are suggested. The majority of the particles seem to originate from coal combustion, which conforms to Taiyuan’s industrial structure

Interpolation in non-positively curved K\"ahler manifolds

We extend to any simply connected K\"ahler manifold with non-positive sectional curvature some conditions for interpolation in $\mathbb{C}$ and in the unit disk given by Berndtsson, Ortega-Cerd\`a and Seip. The main tool is a comparison theorem for the Hessian in K\"ahler geometry due to Greene, Wu and Siu, Yau.Comment: 9 pages, Late

Divided Differences & Restriction Operator on Paley-Wiener Spaces PWtaupPW_{tau}^{p} for N−N-Carleson Sequences

For a sequence of complex numbers $\Lambda$ we consider the restriction operator $R_{\Lambda}$ defined on Paley-Wiener spaces $PW_{\tau}^{p}$ ($1<p<\infty$). Lyubarskii and Seip gave necessary and sufficient conditions on $\Lambda$ for $R_{\Lambda}$ to be an isomorphism between $PW_{\tau}^{p}$ and a certain weighted $l^{p}$ space. The Carleson condition appears to be necessary. We extend their result to $N-$Carleson sequences (finite unions of $N$ disjoint Carleson sequences). More precisely, we give necessary and sufficient conditions for $R_{\Lambda}$ to be an isomorphism between $PW_{\tau}^{p}$ and an appropriate sequence space involving divided differences