951 research outputs found
Trace ideals for Fourier integral operators with non-smooth symbols II
We consider Fourier integral operators with symbols in modulation spaces and
non-smooth phase functions whose second orders of derivatives belong to certain
types of modulation space. We establish continuity and Schatten-von Neumann
properties of such operators when acting on modulation spaces.Comment: 25 page
Cyclical Consumption Patterns and Rational Addiction
Series: Department of Economics Working Paper Serie
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
Local well-posedness for the nonlinear Schr\"odinger equation in the intersection of modulation spaces
We introduce a Littlewood-Paley characterization of modulation spaces and use
it to give an alternative proof of the algebra property, somehow implicitly
contained in Sugimoto (2011), of the intersection for , and
. We employ this algebra property to show the local well-posedness of
the Cauchy problem for the cubic nonlinear Schr\"odinger equation in the above
intersection. This improves Theorem 1.1 by B\'enyi and Okoudjou (2009), where
only the case is considered, and closes a gap in the literature. If and or if and then
and the
above intersection is superfluous. For this case we also reobtain a
H\"older-type inequality for modulation spaces.Comment: 14 page
Periodic and discrete Zak bases
Weyl's displacement operators for position and momentum commute if the
product of the elementary displacements equals Planck's constant. Then, their
common eigenstates constitute the Zak basis, each state specified by two phase
parameters. Upon enforcing a periodic dependence on the phases, one gets a
one-to-one mapping of the Hilbert space on the line onto the Hilbert space on
the torus. The Fourier coefficients of the periodic Zak bases make up the
discrete Zak bases. The two bases are mutually unbiased. We study these bases
in detail, including a brief discussion of their relation to Aharonov's modular
operators, and mention how they can be used to associate with the single degree
of freedom of the line a pair of genuine qubits.Comment: 15 pages, 3 figures; displayed abstract is shortened, see the paper
for the complete abstrac
The finiteness of the four dimensional antisymmetric tensor field model in a curved background
A renormalizable rigid supersymmetry for the four dimensional antisymmetric
tensor field model in a curved space-time background is constructed. A closed
algebra between the BRS and the supersymmetry operators is only realizable if
the vector parameter of the supersymmetry is a covariantly constant vector
field. This also guarantees that the corresponding transformations lead to a
genuine symmetry of the model. The proof of the ultraviolet finiteness to all
orders of perturbation theory is performed in a pure algebraic manner by using
the rigid supersymmetry.Comment: 23 page
Rise and diversification of chondrichthyans in the Paleozoic
The Paleozoic represents a key time interval in the origins and early diversification of chondrichthyans (cartilaginous fishes), but their diversity and macroevolution are largely obscured by heterogenous spatial and temporal sampling. The predominantly cartilaginous skeletons of chondrichthyans pose an additional limitation on their preservation potential and hence on the quality of their fossil record. Here, we use a newly compiled genus-level dataset and the application of sampling standardization methods to analyze global total-chondrichthyan diversity dynamics through time from their first appearance in the Ordovician through to the end of the Permian. Subsampled estimates of chondrichthyan genus richness were initially low in the Ordovician and Silurian but increased substantially in the Early Devonian. Richness reached its maximum in the middle Carboniferous before dropping across the Carboniferous/Permian boundary and gradually decreasing throughout the Permian. Sampling is higher in both the Devonian and Carboniferous compared with the Silurian and most of the Permian stages. Shark-like scales from the Ordovician are too limited to allow for some of the subsampling techniques. Our results detect two Paleozoic radiations in chondrichthyan diversity: the first in the earliest Devonian, led by acanthodians (stem-group chondrichthyans), which then decline rapidly by the Late Devonian, and the second in the earliest Carboniferous, led by holocephalans, which increase greatly in richness across the Devonian/Carboniferous boundary. Dispersal of chondrichthyans, specifically holocephalans, into deeper-water environments may reflect a niche expansion following the faunal displacement in the aftermath of the Hangenberg extinction event at the end of the Devonian
Fellow prisoners
La Facultat de Filosofia i Lletres de la UAB publica, des de principis del confinament pel Covid-19, una sèrie de píndoles en forma de breu article, sota el títol 'Llibres i música en temps de desassossec', on es convida al lector a conèixer diferents suggeriments per a la lectura o l'audició de música, que ajudin a millorar l'estat d'ànim i aportin coneixement en moments difícils i d'incertesa per a tots. A 'Llibres i música en temps de desassossec' es poden llegir textos de professors i professores de la FacultatText publicat com a notícia a la web de la Facultat de Filosofia i Lletres de la Universitat Autònoma de Barcelona el 29/06/202
An optimally concentrated Gabor transform for localized time-frequency components
Gabor analysis is one of the most common instances of time-frequency signal
analysis. Choosing a suitable window for the Gabor transform of a signal is
often a challenge for practical applications, in particular in audio signal
processing. Many time-frequency (TF) patterns of different shapes may be
present in a signal and they can not all be sparsely represented in the same
spectrogram. We propose several algorithms, which provide optimal windows for a
user-selected TF pattern with respect to different concentration criteria. We
base our optimization algorithm on -norms as measure of TF spreading. For
a given number of sampling points in the TF plane we also propose optimal
lattices to be used with the obtained windows. We illustrate the potentiality
of the method on selected numerical examples
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