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

Olteanu M.

11th WSEAS International Conference on Automatic Control, Modelling and Simulation, İstanbul, Türkiye, 30 Mayıs - 01 Haziran 2009, ss.199-200 identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.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.