Time-invariant Systems on Hilbert spaces through convolution and multiplication Representations

Olteanu M.

11th WSEAS International Conference on Automatic Control, Modelling and Simulation, İstanbul, Turkey, 30 May - 01 June 2009, pp.199-200 identifier

  • Publication Type: Conference Paper / Full Text
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.199-200


As is well known, every L-2 time-invariant input-output map admits a Multiplicative representation in the frequency domain. In time domain, under additional hypotheses, Such operator reduces to a convolution operation. By using Mackey's imprimitivity systems, an attempt is made in order to generalize these facts to time-invariant bounded linear systems oil arbitrary Hilbert spaces. This initiative leads to a complete characterization of abstract time-invariant systems. Further, connections between causality and Mackey's imprimitivity Theorem are investigated as well. The main result is a property of invariance of causal systems under Mackey's representation theorem of systems of imprimitivity.