15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien

Sektion 7 - Funktionalanalysis, Harmonische Analysis
Montag, 17. September 2001, 17.30, Hörsaal 28


Modulation spaces and ultra-distributions

Nenad Teofanov, University of Novi Sad (Koautor: Stevan Pilipovic)


For the study of local properties of objects in phase space (time-frequency domain) it is convenient to use modulation spaces. Existing literature concerning modulation spaces confirms their importance both from the theoretical and the practical point of view [1], [2]. In this short lecture we show that modulation spaces enable an elegant approach to various spaces of tempered distributions and ultradistributions [3], [4]. In this context the difference between modulation spaces using polynomial or almost exponential weights becomes more clear.

[1] H. G. Feichtinger, T. Strohmer (editors): Gabor Analysis and Algorithms, Birkhäuser, Boston, Basel, Berlin, 1998.
[2] K. Gröchenig: Foundations of Time-Frequency Analysis, Birkhäuser, Boston, Basel, Berlin, 2001.
[3] H. G. Feichtinger, K. Gröchenig, D. Walnut: Wilson Bases and modulation spaces, Math. Nach. 155:7-17, 1992.
[4] S.Pilipovic, N. Teofanov: Wilson Bases and ultramodulation spaces, Math. Nach. to appear.

E-Mail: tnenad@unsim.im.ns.ac.yu

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