ESI12

Modern Methods of TimeFrequency 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
1721 SEP 2012
Coorbit theory is by now a wellestablished 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
Gabortransform 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, AntiWick and Berezin Calculus
 Operators described using atomic decompositions, localization theory
 Numerics of coorbit spaces, computational (and storage) aspects...
 groupfree coorbit theory (sections, alphamodulation spaces),....
see
» program

 