Mathematics Department Colloquium
The Mathematics Department Colloquium meets periodically throughout the academic year.
Latest colloquium information for the 2011-2012 academic year:
Sergei Avdonin*
Department of Mathematics
University of Alaska FairbanksMonday, April 2, Holt 124**, 2:00-3:00 pm.
Nonharmonic Fourier Series in Control Theory and Signal Processing
Abstract. The goal of this talk is to describe connections between nonharmonic Fourier series, control theory, inverse problems of mathematical physics, and signal processing. In particular, we describe some classical and recent results on exponential bases and their applications to control theory. We discuss also an approach to inverse problems (the so-called Boundary Control Method) which is based on deep connections between controllability and identification problems and is applicable to a wide range of linear systems.
As an example of the approach, we consider control and inverse problems for differential equations on graphs. We suppose that on each edge of the graph the wave (or heat, or Schrödinger) equation is defined, and that some compatibility conditions are satisfied at the internal vertices. We investigate boundary controllability and boundary identifiability of the system.
We demonstrate effectiveness of the Boundary Control Method on a classical problem of signal processing --- the spectral estimation problem. Sampling and interpolation problems of band-limited and multi-band signals will also be discussed.
*Professor Avdonin is a candidate for the position of Unum Chair of Excellence in Applied Mathematics.
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