In the following you will find a list of research projects carried out at NUHAG.

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X Continuous and discrete Gabor frames FWF CdGF 2009.01 2011.12
FWF project with project-leader Norbert Kaiblinger
Time-frequency analysis is a flourishing mathematical topic. Time-frequency analytic techniques are successfully applied in various fields, such as quantum physics, electrical engineering, seismic geology, radar, mobile communications, or the analysis of biometrical data. Because of their interdisciplinary origin, these techniques appeal to scientists and engineers of many different backgrounds. The typical functional analytic model in time-frequency analysis are Gabor frames in a continuous-time setting. On the other hand in applications the attention is often put on discrete models, computational methods, and numerical results.

We establish a link between the continuous and the discrete setting. The use of the discrete model is threefold. First, there are important approximation results that describe a continuous Gabor frame as a limit of discrete Gabor frames. Thus the discrete model has direct implications for the continuous theory. Secondly, the discrete and continuous theory often leads to analogous problems. Thus even in absence of direct approximate implications the discrete analysis contributes to understanding the continuous problem by analogy. Thirdly, as indicated above, discrete Gabor frames are highly relevant for applications and thus the discrete setting is an area of interest in its own right. In fact, we will also describe discrete phenomena that do not have an obvious continuous analogue.

ANB ... Austrian National Bank
EC ...European Commission
FWF ... Fonds zur Förderung der wissenschaftlichen Forschung
UniVie ... University of Vienna
WWTF ... Wiener Wissenschafts-, Forschungs- und Technologiefonds