Wolfgang Pauli Institute (WPI) Vienna 


 
Topics: TBA  

Paul, Thierry  Seminar room C 714  Tue, 25. Nov 08, 13:15 
"Delocalization"  

Athanassoulis, Agissilaos  Seminar room C 714  Tue, 25. Nov 08, 14:00 
"Regularization of semiclassical limits in terms of smoothed Wigner transforms"  
Phasespace methods such as Wigner transforms have long been used for the study of semiclassical limits. Regularized objects, such as Husimi transforms, have often been proposed as an interesting alternative, but have not been widely used, due to the lack of an appropriate framework to study the equations governing them.  

Nicola, Fabio  Seminar room C 714  Tue, 25. Nov 08, 14:50 
"Boundedness of Fourier integral operators on FourierLebesgue spaces and related topics"  
Note: Abstract  

Kaiblinger, Norbert  Seminar room C 714  Wed, 26. Nov 08, 9:30 
"Some elements of FeichtingerGroechenig theory and their use in timefrequency analysis"  
Several deep results in timefrequency analysis, known as FeichtingerGroechenig theory, are crucial for understanding Gabor frames. We point out a few aspects.  

de Gasson, Maurice  Seminar room C 714  Wed, 26. Nov 08, 10:25 
"Density Operators and the Uncertainty Principle"  

Strohmer, Thomas  Seminar room C 714  Wed, 26. Nov 08, 11:15 
"From Helmholtz to Heisenberg: Sparse Remote Sensing"  

Hlawatsch, Franz  Seminar room C 714  Wed, 26. Nov 08, 13:30 
"The Wigner distribution: Cross terms, smoothing, and signal synthesis"  
Informal discussion, in order to share experience of the speaker on the subject (dating back to his PhD work and habilitation at TU Vienna) with the workshop participants.  

Athanassoulis, Agissilaos  Seminar room C 714  Wed, 26. Nov 08, 14:10 
"On the computation of smoothed Wigner transforms"  
In the 90's there was wide interest in the use of Wigner and smoothed Wigner transforms in signal processing; several libraries for their computation were created at that time. However, it is fair to say that these transforms are not as widely used today, and one of the reasons is that their computation is "unreasonably" expensive, when compared e.g. to spectrograms. Motivated by a recent scheme for the simulation of caustic development and propagation, we present a new library for the computation of Wigner and smoothed Wigner transforms. The main improvement in comparison to the state of the art is a parallelization of all steps of the process (including output, e.g. plotting) which allows a better behavior for much larger signals.  

Makrakis, George  Seminar room C 714  Wed, 26. Nov 08, 15:05 
"Evolution of semiclassical Wigner functions (the higher dimensional case)"  
ABSTRACT: The limit Wigner measure of a WKB function satisfies a simple transport equation in phasespace and is well suited for capturing oscillations at scale of order $O(epsilon)$, but it fails, for instance, to provide the correct amplitude on caustics where different scales appear. We define the semiclassical Wigner function of an $N$dimensional WKB function, as a suitable formal approximation of its scaled Wigner function. The semiclassical Wigner function is an oscillatory integral that provides an $epsilon$dependent regularization of the limit Wigner measure, it obeys a transportdispersive evolution law in phase space, and it is well defined even at simple caustics.  

Labate, Demetrio  NuHAG, Alserbachstraße 23/ R8  Wed, 26. Nov 08, 16:30 
"Analysis of Singularities and Edge Detection using the Continuous Shearlet Transform"  
It is well known that the continuous wavelet transform has the ability to identify the set of singularities of a function or distribution. It was recently shown that certain multidimensional generalizations of the wavelet transform are useful to capture additional information about the geometry of the singularities.  

Toft, Joachim  Seminar room C 714  Thu, 27. Nov 08, 9:30 
"Weyl product and twisted convolution for timefrequency spaces and modulation spaces"  
The Weyl calculus is an important part within the theory of pseudodifferential operators. In physics, the calculus links classcal mechanics with quantum mechanics in the sense that an observable in classical mechanics corresponds to an operator in quantum mechanics. In general, this operator is the Weyl operator, at least with good approximations.  

Johansson, Karoline  Seminar room C 714  Thu, 27. Nov 08, 10:30 
"A counter example on nontangential convergence for oscillatory integrals"  
Consider the solution to the timedependent Schrödinger equation with initial data f. It is shown by Sjögren and Sjölin in 1989 that there exists f in the Sobolev space $H^s(mathbb{R}^n), ; s=n/2$ such that tangential convergence can not be widened to convergence regions. We show that the corresponding result holds when $Delta_x$ is replaced by an operator $varphi(D)$, with special conditions on $varphi$. More explicitly we consider the solution to the equation $(varphi(D)+ipartial_t )u =0,$ with the initial condition u(x,0)=f(x). Here $varphi$ should be realvalued and its radial derivatives of first and second order ($varphi' =varphi'_r$ and $varphi'' =varphi''_{rr}$) should be continuous, outside a compact set containing origin. Furthermore, we will require some appropriate conditions on the growth $varphi'$ and $varphi''$. In particular the function $varphi(xi)=xi^a$ will satisfy these conditions, for a> 1.  

Teofanov, Nenad  Seminar room C 714  Thu, 27. Nov 08, 11:15 
"Remarks on a class of symbol global type operators"  
We consider a class of pseudodifferential operators defined by smooth symbols which may have almost exponential growth or decay at infinity in phase space. They can be considered as symbolglobal type operators, studied by many authors in the context of PDE. In the present lecture, we use timefrequency methods/Gabor frames in the study of spectral asymptotics. Almost exponential growth/decay of symbols is handled by the use of techniques from ultradistribution theory.  

Mauser, Norbert J.  Seminar room C 714  Thu, 27. Nov 08, 13:30 
"On the time evolution of Wigner measures for Schroedinger equations"  
Our aim is to emphasize the main known limitations to the use of Wigner measures for Schr"odinger equations.  

Feichtinger, Hans G.  Seminar room C 714  Thu, 27. Nov 08, 14:25 
"Banach Gelfand Triples and constructive approximations of continuous problems"  
The setting of the Banach Gelfand triple (S0,L2,SO') allows to describe in a clean functional analytic way how a given continuous problem (such as applying a pseudodifferential operator given by its KohnNirenberg symbol that should be applied to a given L2function, or finding the spreading function of an operator) can be approximated at least in a qualitative way in a constructive way. The setting involves the use of function spaces, Fourier transforms and generalized functions, and aims at the reduction of a continuous problem to a finitedimensional setting, which in principle is available for numerical implementation, e.g. using MATLAB or any other mathematical software.  

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