 CARMA COLLOQUIUM
 Speaker: Prof Brigitte ForsterHeinlein, University of Passau
 Title: The commutative diagram of signal processing
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Tue, 31^{st} Oct 2017
 Abstract:
We consider variations on the commutative diagram consisting of the Fourier transform, the Sampling Theorem and the PaleyWiener Theorem. We start from a generalization of the PaleyWiener theorem and consider entire functions with specific growth properties along halflines. Our main result shows that the growth exponents are directly related to the shape of the corresponding indicator diagram, e.g., its side lengths. Since many results from sampling theory are derived with the help from a more general function theoretic point of view (the most prominent example for this is the PaleyWiener Theorem itself), we motivate that a closer examination and understanding of the Bernstein spaces and the corresponding commutative diagrams can—via a limiting process to the straight line interval [−A,A]—yield new insights into the Lp(R)sampling theory. This is joint work with Gunter Semmler, Technische Universität Bergakademie Freiberg, Germany.
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