On the representation of linear system time‐varying half‐line maps | Zendy

Sandberg Irwin W. | Zendy

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On the representation of linear system time‐varying half‐line maps

Author(s) -

Sandberg Irwin W.

Publication year - 2006

Publication title -

international journal of circuit theory and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.364

H-Index - 52

eISSN - 1097-007X

pISSN - 0098-9886

DOI - 10.1002/cta.370

Subject(s) - representation (politics) , integrable system , bounded function , lebesgue integration , mathematics , real line , function (biology) , space (punctuation) , expression (computer science) , line (geometry) , limit (mathematics) , bounded variation , locally integrable function , mathematical analysis , pure mathematics , computer science , geometry , evolutionary biology , politics , political science , law , biology , programming language , operating system

An expression is given for the most general continuous causal linear input–output map that takes the space of (Lebesgue) integrable functions into itself. This expression is a function‐space limit of an integral. As an application, a representation result is given for an important family of linear maps that take the space of bounded measurable functions into itself and satisfy a certain continuity condition. Some related material concerning engineering education is also given. Copyright © 2006 John Wiley & Sons, Ltd.

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