229 research outputs found
Co-compact Gabor systems on locally compact abelian groups
In this work we extend classical structure and duality results in Gabor
analysis on the euclidean space to the setting of second countable locally
compact abelian (LCA) groups. We formulate the concept of rationally
oversampling of Gabor systems in an LCA group and prove corresponding
characterization results via the Zak transform. From these results we derive
non-existence results for critically sampled continuous Gabor frames. We obtain
general characterizations in time and in frequency domain of when two Gabor
generators yield dual frames. Moreover, we prove the Walnut and Janssen
representation of the Gabor frame operator and consider the Wexler-Raz
biorthogonality relations for dual generators. Finally, we prove the duality
principle for Gabor frames. Unlike most duality results on Gabor systems, we do
not rely on the fact that the translation and modulation groups are discrete
and co-compact subgroups. Our results only rely on the assumption that either
one of the translation and modulation group (in some cases both) are co-compact
subgroups of the time and frequency domain. This presentation offers a unified
approach to the study of continuous and the discrete Gabor frames.Comment: Paper (v2) shortened. To appear in J. Fourier Anal. App
Reproducing formulas for generalized translation invariant systems on locally compact abelian groups
In this paper we connect the well established discrete frame theory of
generalized shift invariant systems to a continuous frame theory. To do so, we
let , , be a countable family of closed, co-compact
subgroups of a second countable locally compact abelian group and study
systems of the form with generators in and with each
being a countable or an uncountable index set. We refer to systems of this form
as generalized translation invariant (GTI) systems. Many of the familiar
transforms, e.g., the wavelet, shearlet and Gabor transform, both their
discrete and continuous variants, are GTI systems. Under a technical
local integrability condition (-LIC) we characterize when GTI systems
constitute tight and dual frames that yield reproducing formulas for .
This generalizes results on generalized shift invariant systems, where each
is assumed to be countable and each is a uniform lattice in
, to the case of uncountably many generators and (not necessarily discrete)
closed, co-compact subgroups. Furthermore, even in the case of uniform lattices
, our characterizations improve known results since the class of GTI
systems satisfying the -LIC is strictly larger than the class of GTI
systems satisfying the previously used local integrability condition. As an
application of our characterization results, we obtain new characterizations of
translation invariant continuous frames and Gabor frames for . In
addition, we will see that the admissibility conditions for the continuous and
discrete wavelet and Gabor transform in are special cases
of the same general characterizing equations.Comment: Minor changes (v2). To appear in Trans. Amer. Math. So
Density and duality theorems for regular Gabor frames
We investigate Gabor frames on locally compact abelian groups with
time-frequency shifts along non-separable, closed subgroups of the phase space.
Density theorems in Gabor analysis state necessary conditions for a Gabor
system to be a frame or a Riesz basis, formulated only in terms of the index
subgroup. In the classical results the subgroup is assumed to be discrete. We
prove density theorems for general closed subgroups of the phase space, where
the necessary conditions are given in terms of the "size" of the subgroup. From
these density results we are able to extend the classical Wexler-Raz
biorthogonal relations and the duality principle in Gabor analysis to Gabor
systems with time-frequency shifts along non-separable, closed subgroups of the
phase space. Even in the euclidean setting, our results are new
Steady-state initialization of object-oriented thermo-fluid models by homotopy methods
The steady-state initialization of large object-oriented
thermo-hydraulic networks is a difficult problem, because of the sensitivity of the convergence to the initial guesses of the iteration variables. This paper proposes an approach to this problem based on homotopy transformation, detailing specific criteria for model simplifications in this physical domain. The approach is successfully demonstrated on large power plant test cases, having several hundreds of iteration variables
Sampling and periodization of generators of Heisenberg modules
This paper considers generators of Heisenberg modules in the case of twisted
group -algebras of closed subgroups of locally compact abelian groups and
how the restrction and/or periodization of these generators yield generators
for other Heisenberg modules. Since generators of Heisenberg modules are
exactly the generators of (multi-window) Gabor frames, our methods are going to
be from Gabor analy\-sis. In the latter setting the procedure of restriction
and periodization of generators is well known. Our results extend this
established part of Gabor analy\-sis to the general setting of locally compact
abelian groups. We give several concrete examples where we demonstrate some of
the consequences of our results. Finally, we show that vector bundles over an
irrational noncommutative torus may be approximated by vector bundles for
finite-dimensional matrix algebras that converge to the irrational
noncommutative torus with respect to the module norm of the generators, where
the matrix algebras converge in the quantum Gromov-Hausdorff distance to the
irrational noncommutative torus
Das Staatsarchiv Hamburg und die Personenforschung in der NS-Zeit
Das Staatsarchiv Hamburg feierte 2010 sein 300-jähriges Bestehen.
Sein Vorläufer wurde bereits im Jahre 1293 erstmals erwähnt und somit die Aufbewahrung wichtiger Dokumente der Stadt an zentraler Stelle bezeugt. Doch erst seit dem 11. September 1710, dem Amtsantritt von Nicolaus Stampeel als wissenschaftlicher Archivar bei der Stadt Hamburg, werden Dokumente systematisch ausgewählt, bewahrt und erschlossen.
Dieses Jubiläum hat das Staatsarchiv mit einem breit gefächerten Veranstaltungsprogramm begangen, zu dem auch Vorträge und Lesungen gehörten, die in der hier vorliegenden Festschrift abgedruckt sind.In 2010, the Hamburg State Archives celebrated its 300th anniversary. The Archives\u27 forerunner was first mentioned in 1293 and thus testified to the preservation of important documents of the city in a central place. But it was not until September 11th, 1710, when Nicolaus Stampeel took office as a scientific archivist at the City of Hamburg. From then on, documents were systematically selected, preserved and indexed.
This anniversary was celebrated by the State Archives with a broad programme of events, which included lectures and readings printed in the commemorative volume available here
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