In this paper equivalent conditions for exact observability of diagonal systems with a one-dimensional output operator are given. One of these equivalent conditions is the conjecture of Russell and Weiss (1994). The other conditions are given in terms of the eigenvalues and the Fourier coefficients of the system data.
Faculty of Mathematical Sciences, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
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