A number of basic elements for a system theory of linear, shift-invariant systems on L/sub 1/(0, infinity ) are presented. The framework is developed from first principles and considers a linear system to be a linear (possibly unbounded) operator on L/sub 2/(0, infinity ). The properties of causality and stabilizability are studied in detail, and necessary and sufficient conditions for each are obtained. The idea of causal extendibility is discussed and related to operators defined on extended spaces. Conditions for w-stabilizability and w-stability are presented. The graph of the system (operator) will play a unifying role in the definitions and results. The authors discuss the natural partial order on graphs (viewed as subspaces) and its relevance to systems theory.
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机译：提出了关于L / sub 1 /（0，infinity）上的线性，位移不变系统的系统理论的许多基本要素。该框架是根据第一原理开发的，认为线性系统是L / sub 2 /（0，infinity）上的线性（可能是无界的）算子。对因果关系和稳定性的性质进行了详细研究，并为它们各自提供了必要和充分的条件。讨论了因果可扩展性的思想，并将其与在扩展空间上定义的运算符有关。给出了w稳定性和w稳定性的条件。系统（操作员）的图形将在定义和结果中扮演统一的角色。作者讨论了图（被视为子空间）上的自然偏序及其与系统理论的关系。
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