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

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

Cornerstones of Sampling of Operator Theory

This paper reviews some results on the identifiability of classes of operators whose Kohn-Nirenberg symbols are band-limited (called band-limited operators), which we refer to as sampling of operators. We trace the motivation and history of the subject back to the original work of the third-named author in the late 1950s and early 1960s, and to the innovations in spread-spectrum communications that preceded that work. We give a brief overview of the NOMAC (Noise Modulation and Correlation) and Rake receivers, which were early implementations of spread-spectrum multi-path wireless communication systems. We examine in detail the original proof of the third-named author characterizing identifiability of channels in terms of the maximum time and Doppler spread of the channel, and do the same for the subsequent generalization of that work by Bello. The mathematical limitations inherent in the proofs of Bello and the third author are removed by using mathematical tools unavailable at the time. We survey more recent advances in sampling of operators and discuss the implications of the use of periodically-weighted delta-trains as identifiers for operator classes that satisfy Bello's criterion for identifiability, leading to new insights into the theory of finite-dimensional Gabor systems. We present novel results on operator sampling in higher dimensions, and review implications and generalizations of the results to stochastic operators, MIMO systems, and operators with unknown spreading domains

Quantum theta functions and Gabor frames for modulation spaces

Representations of the celebrated Heisenberg commutation relations in quantum mechanics and their exponentiated versions form the starting point for a number of basic constructions, both in mathematics and mathematical physics (geometric quantization, quantum tori, classical and quantum theta functions) and signal analysis (Gabor analysis). In this paper we try to bridge the two communities, represented by the two co--authors: that of noncommutative geometry and that of signal analysis. After providing a brief comparative dictionary of the two languages, we will show e.g. that the Janssen representation of Gabor frames with generalized Gaussians as Gabor atoms yields in a natural way quantum theta functions, and that the Rieffel scalar product and associativity relations underlie both the functional equations for quantum thetas and the Fundamental Identity of Gabor analysis.Comment: 38 pages, typos corrected, MSC class change