Math.Koll. am 3.5.06/Dr. Wojciech Czaja

Institut für Mathematik sekr.mathematik at
Mon Apr 24 14:12:40 CEST 2006

Mathematisches Kolloquium


zu einem


im Rahmen der Habilitation

Dr. Wojciech Czaja
(Fakultaet fuer Mathematik, Universitaet Wien)

mit dem Thema:
"Beurling dimension and wave packets of cordoba and Fefferman"

We study wave packets, that is countable collections of dilations,
translations, and modulations of a single square integrable function. The
parameters of these unitary actions form a discrete subset of the
Weyl-Heisenberg affine group.

For the purpose of this study, we introduce analogues of the notion of
Beurling density for discrete subsets of the Euclidean space. From this we
derive the notion of the Beurling dimension and we study its properties.

Next, we adapt the notion of Beurling dimension to the geometry of discrete
subsets of the Weyl-Heisenberg affine group. Our goal is to describe
completeness properties of wave packets via geometric properties of the sets
of their parameters. In particular, we show necessary conditions for a wave
packet to be a Bessel system, and we construct multiple examples of
non-standard wave packets with prescribed dimensions.

Zeit: Mittwoch, 3. Mai 2006, 16.15 Uhr

Ort: Fakultaet fuer Mathematik der Universitaet Wien, Nordbergstr. 15,
       Seminarraum C 2.09

Harald Rindler
Hans Georg Feichtinger

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