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UID:8302@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20140915T100000
DTEND;TZID=Europe/Paris:20140915T110000
DTSTAMP:20241120T210329Z
URL:https://www.i2m.univ-amu.fr/evenements/banach-gelfand-triples-and-thei
 r-use-in-fourier-analysis/
SUMMARY:Hans G. Feichtinger (Institute of Mathematics\, University of Vienn
 a): Banach Gelfand Triples and their use in Fourier Analysis
DESCRIPTION:Hans G. Feichtinger: Banach Gelfand triples are triples of Bana
 ch spaces included in each other in a very special way: Formally one assum
 es that there is an embedding of a Banach space (of test functions) into i
 ts dual (a Banach space of generalized functions)\, with a Hilbert space i
 n the middle. There is a specific Banach Gelfand triple\, based on the Seg
 al Algebra S0(ℝd) (in fact it can be defined for general LCA groups)\, w
 hich has its roots in time-frequency analysis. In fact\, this space (and i
 ts dual as well as the intermediate Hilbert space L2(ℝd)) are so-called 
 modulation spaces and can be characterized via their Gabor coefficients. T
 his BGT is suitable in describing the Fourier transform in a general way\,
  but also the transition from operators to their spreading representation.
  One of the cornerstones is the analog of matrix representations for linea
 r mappings on ℝn: the so-called kernel theorem\, where one usually has t
 o resort to the Schwartz space of rapidly descreasing function\, a prototy
 pe of a nuclear Frechet space (hence not a Banach space!).\n\nhttps://www.
 youtube.com/watch?v=zG2IDsIbpFk
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Hans_Georg_Feichtinger.jpg
CATEGORIES:Séminaire,Analyse et Géométrie
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