"Symmetries of decomposition spaces"Führ, HartmutDecomposition spaces of Besov type are a class of function spaces that are able to capture the approximation-theoretic properties of a large variety of dictionaries such as generalized wavelet transforms in arbitrary dimensions, Gabor systems, wave packet systems, etc. The scales of spaces that can be treated by the decomposition space approach include Besov spaces (isotropic and anisotropic versions) and modulation spaces. Understanding symmetries of such spaces, i.e. invariance properties under fundamental operations such as composition by a matrix, is a fundamental question in this domain. In this talk we present a general approach to tackle it, and answers for a variety of settings. The talk is based on joint work with Rene Koch, Reihaneh Raisi-Tousi, Jordy van Velthoven and Felix Voigtlaender. |
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