Modern Methods of Time-Frequency Analysis II
September 10th to December 15th, 2012
Erwin Schroedinger Institute (Univ. Vienna)

Workshop: [W1] Applied Coorbit theory 
organized by Stephan Dahlke and Hans G. Feichtinger
17-21 SEP 2012

Coorbit theory is by now a well-established tool in applied harmonic analysis. Based on group representations, this theory provides a unified approach that collects many different transforms such as the wavelet- and the Gabor-transform under one roof. Furthermore, the coorbit approach provides canonical smoothness spaces, the coorbit spaces. It is one of the aims of this workshop to strive for a complete classification of all possible coorbit spaces.

Moreover, the coorbit theory provides atomic decompositions for the coorbit spaces by means of stable (Banach) frame decompositions. In many cases, the coorbit spaces coincide with classical smoothness spaces such as Besov and modulation spaces. For these spaces, many different atomic and molecular decompositions exist. Therefore, an additional aim of this workshop is to clarify the relations of these different decomposition techniques as far as possible

In recent years, also the relations of coorbit theory with operator equations has become a center of attention. E.g., the theory of coorbit atoms and molecules can be exploited to clarify the mapping properties of operators as well as their localization properties. Moreover, there are approaches to use the coorbit ideas also for the numerical treatment of operator equations. Therefore, there is an urgent need for fast algorithms etc. It is an additional goal of this workshop to discuss the state of the art in computational coorbit theory as well as the further perspectives.

Therefore, the topics to be discussed include (but are not limited to)
  • Classification of Coorbit families (groups, representations, etc.)
  • Coorbit spaces, discretization, atomic decomposition, molecular
  • Toeplitz operators, Anti-Wick and Berezin Calculus
  • Operators described using atomic decompositions, localization theory
  • Numerics of coorbit spaces, computational (and storage) aspects...
  • group-free coorbit theory (sections, alpha-modulation spaces),....

see » program