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Coorbit Theory and Generalizations (Banach Frames) (1481)
25 August – 7 September 2014 at CIRM (Marseille Luminy, France)
  • Banach frames
  • Non-orthogonal exoansions
  • Toeplitz operators
  • Atomic and localized expansions

Coorbit  theory  was  developed  originally  as  a  unifying  principle for the results in wavelet theory (continuous wavelet transform, atomic decompositions). More recently a number of new examples have been proposed, using new groups and different settings, sometimes deviating significantly from the classical approach, starting from an irreducible and integrable group representation. Shearlets and Blaschke groups indicate  the  use  of new  groups,  while other results establish closer ties between complex and harmonic analysis, or the theory of polyanalytic functions. In all cases, one finds atomic decompositions of the elements of the corresponding  coorbit  spaces using well localized building blocks. More recently, connections to solutions of the heat equation over Riemannian manifolds and spaces of homogenous type are emerging and ask for detailed investigations of the analogies and similarities between the different settings. Moreover, Toeplitz operators (obtained by a composition of a multiplication operator with a projection operator) play an important role and provide a link to the theory of operator algebras. The workshop brought together a group of well-established researchers from the different branches mentioned, in order to do some ground-breaking work helping to unify the independent approaches taken by the different sub-communities doing research in this area.