Abstract: In classical wavelet analysis, a multiresolution analysis (MRA) is a discrete time-frequency decomposition of L^2-functions on a euclidean vector space given by pairing with dilations and translations of certain basis functions (wavelets). In this talk, we briefly recapitulate the classical concepts and then introduce a radial multiresolution for the space of unitarily invariant L^2-functions on the space of hermitian matrices. This space can be identified with a weighted L^2-space on a closed Weyl chamber of type A (the ordered spectrum). A key ingredient is the definition of a generalized translation preserving this radial geometry. Some knowledge about the fine structure of this translation, based on results by Graczyk, Sawyer and Loeb, is needed in order to obtain basic properties of the radial MRA. We characterize orthonormal wavelet bases and prove their existence. This talk is based on joint results with M. Rösler.
Bei Interesse an einer online-Teilnahme (sei es regelmäßig oder auch nur an einem bestimmten Vortrag) bitten wir vorab mit Tobias Weich oder Benjamin Delarue Kontakt aufzunehmen, damit der Teilnahmelink geteilt werden kann.