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Special voice transforms and applications

The general goal of this project is to study the properties of the voice transforms generated by the representations of a given locally compact topological group, to reveal the details and understand the mathematical principles that govern the approximation of functions using discrete frames and wavelets, Zernike functions, spherical functions, construction of multi-resolution decompositions. Applications of these processes will be considered. In the theoretical analysis we will focus on particular examples of voice transforms and the study of the properties of these transforms. One aim will be the constructions of discrete rational wavelets and frames. After the theoretical development the numerical aspects will be also studied using the MATLAB and MATHEMATICA. Our aim is to study properties which are outlined in the general theory developed by Feichtinger and Gröchenig in the case of the voice transforms generated by the representations of the Blaschke group, and other groups, generated by other representations.
Department of Mathematics
University of Vienna
Alserbachstrasse 23
A-1090, Vienna AUSTRIA

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