Mathematik-Gebäude, Raum M614

In Gabor analysis one studies the construction and properties of series expansions of functions with respect to a set of time-frequency shifts (phase space shifts) of a single function. Such expansions, which are nowadays called Gabor series, arise in quantum mechanics as coherent state expansions, in wireless communications for orthogonal frequency division multiplexing (OFDM), in operator theory as non-commutative tori. Furthermore, the construction of certain Gabor expansions is equivalent to sampling and interpolation theorems in Bargmann-Fock space in complex analysis. In this talk I will survey the main structure theorems for Gabor frames and Gabor expansions and discuss some classes of Gabor frames. I will try to explain some of the connections to other areas of mathematics.

Der Vortrag wird nach Bedarf auf Deutsch oder Englisch gehalten.

Prof. Dr. Karlheinz Gröchenig

TU Wien