Abstract
This paper is about the causality structure of systems in Hilbert spaces. While treatments on the subjects are usually confined to systems which enjoy properties such as linearity, boundedness, or nonpredictive behavior, here, all these properties play no essential role. As a consequence, new and more general results are obtained. These results concern the concepts of causality, anticausality, and crosscausality, and give necessary and sufficient conditions to decompose a general system into the sum of causal, anticausal, and crosscausal components.
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This research was in part supported by the NSF Grant GK1925 and by the Canadian NRC Grant A8244.
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De Santis, R.M. Causality for nonlinear systems in Hilbert spaces. Math. Systems Theory 7, 323–337 (1973). https://doi.org/10.1007/BF01890607
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DOI: https://doi.org/10.1007/BF01890607