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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.