Discrete Simulation of a Class of Distributed Systems Using Functional Analytic Methods

  • Authors:

  • Vitali Dymkou;Rudolf Rabenstein;Peter Steffen

  • Affiliations:

  • Multimedia Communications and Signal Processing, University of Erlangen-Nuremberg, Erlangen, Germany D-91058;Multimedia Communications and Signal Processing, University of Erlangen-Nuremberg, Erlangen, Germany D-91058;Multimedia Communications and Signal Processing, University of Erlangen-Nuremberg, Erlangen, Germany D-91058

  • Venue:
  • Multidimensional Systems and Signal Processing
  • Year:
  • 2006

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Abstract

This paper investigates the discrete simulation of the solution of initial-boundary-value problems that typically arise in technical areas. Since many of them lead to unbounded and non-self-adjoint differential operators, we have to use a rather general theory as a mathematical basis. For the class of sectorial operators with a compact resolvent operator, the solution of initial-boundary-value problem can be represented by means of a certain holomorphic semigroup. It is shown that the solution can be expanded with respect to the canonical system of the considered operator. Such an expansion corresponds to a multi-dimensional functional transformation in the frequency domain. This fact leads to simple structures for the realization of the resulting system. Computationally efficient numerical algorithms can be derived by proper methods well-known from the theory of digital signal processing.