ELFT HÍRADÓ

[Balog Janos <balog.janos AT wigner.mta.hu>]

MTA Wigner FK RMI Elméleti Osztály Szemináriuma
Tisztelettel meghívjuk


                       Hans Feichtinger
                     (University of Vienna)


 "A function space defined by the Wigner transform and its Applications"


             címmel tartandó szemináriumára.

Kivonat:

The so-called Feichtinger algebra S0, resp.\ the modulation space M1 on 
Rd can be defined by the integrability of the Wigner transform. Despite 
the quadratic character of the transform this defines a linear space and 
even a FOURIER invariant Banach space containing the Schwartz space of 
rapidly decreasing functions.
Based on such a Banach space of test functions one can develop a quite 
general but still comparatively convenient theory of Fourier transforms, 
covering the continuous and discrete, the periodic and the non-periodic 
case.
Using the Banach Gelfand triple, consisting of S0, contained in the 
Hilbert space L2 and this in turn embedded into the space SO′ of linear 
functionals one has a good way to describe questions from applied 
fields, such as slowly varying systems, audio signals (using 
spectrograms) and much more. Moreover it a key element in a variant of 
time-frequency analysis called Gabor Analysis, going back to the work of 
Dennes Gabor (published in 1946).
This Banach Gelfand Triple is a suitable tool for theoretical physics 
(rigged Hilbert space) and time-frequency analysis.
The spaces can also be characterized via so-called Wilson bases, which 
also played a significant role in the signal processing part of the 
discovery of gravitational waves by the LIGO team (Phyiscs Nobel-Prize 
2017).




Helye: MTA Wigner FK RMI III.ép. Tanácsterem
Ideje: 2018 március 2  péntek du. 14:00 óra



Szívesen látunk minden érdeklődőt.

                                            Balog János