Abstract

The techniques of non-self adjoint spectral theory are employed to formulate a frequency domain theory for general linear systems characterized by operators on a (Hilbert) resolution space. The properties and relationships between the various frequency domain representations are studied and the special forms which these representations take when applied to causal and passive operators are delineated. Finally, the theory is illustrated via the formulation of a number of operator decomposition problems in a frequency domain setting and a study of the frequency domain stability problem.

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