Universal usefulness of BUPUs in Harmonic AnalysisHans G. Feichtinger given at OSLO workshop 2013 (15.02.13) id: 2484 length: min status: type: LINK-Presentation: https://nuhagphp.univie.ac.at/dateien/talks/2484_oslo13A.pdf ABSTRACT: BUPUs stands for bounded uniform partitions of unity. It is the purpose of this talk to point out the importance that come from the existence of BUPUs of arbitrary (small) size. On the Euclidean space they can be obtained by compressing (via dilation) any given BUPU, e.g. a partition of unity generated by shifted (say cubic) B-splines. They can be used to proof compactness results, to define Wiener amalgam spaces or modulation spaces, to understand the behavior of Shannon’s sampling theorem, or to show how functions or measures can be approximated by discrete measures (or discrete- periodic signals). |