Resolution Space, Operators and Systems

R. Saeks

ISBN 10: 354006155X / ISBN 13: 9783540061557

Published by Springer, J.B. Metzler Feb 1973, 1973

About this Item

This item is printed on demand - Print on Demand Titel. Neuware -If one takes the intuitive point of view that a system is a black box whose inputs and outputs are time functions or time series it is natural to adopt an operator theoretic approach to the stUdy of such systems. Here the black box is modeled by an operator which maps an input time function into an output time function. Such an approach yields a unification of the continuous (time function) and discrete (time series) theories and simultaneously allows one to formulate a single theory which is valid for time-variable distributed and nonlinear systems. Surprisingly, however, the great potential for such an approach has only recently been realized. Early attempts to apply classical operator theory typically having failed when optimal controllers proved to be non-causal, feedback systems unstable or coupling networks non-lossless. Moreover, attempts to circumvent these difficulties by adding causality or stability constraints to the problems failed when it was realized that these time based concepts were undefined and; in fact, undefinable; in the Hilbert and Banach spaces of classical operator theory.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 284 pp. Englisch.

Seller Inventory # 9783540061557

Bibliographic Details

• Title: Resolution Space, Operators and Systems
• Publisher: Springer, J.B. Metzler Feb 1973
• Publication Date: 1973
• Language: English
• ISBN 10: 354006155X
• ISBN 13: 9783540061557
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 254W x 178H x 16D millimeters 254 millimeters width by 178 millimeters height by 16 millimeters depth
• Weight: 540 grams

About this title

Synopsis

If one takes the intuitive point of view that a system is a black box whose inputs and outputs are time functions or time series it is natural to adopt an operator theoretic approach to the stUdy of such systems. Here the black box is modeled by an operator which maps an input time function into an output time function. Such an approach yields a unification of the continuous (time function) and discrete (time series) theories and simultaneously allows one to formulate a single theory which is valid for time-variable distributed and nonlinear systems. Surprisingly, however, the great potential for such an approach has only recently been realized. Early attempts to apply classical operator theory typically having failed when optimal controllers proved to be non-causal, feedback systems unstable or coupling networks non-lossless. Moreover, attempts to circumvent these difficulties by adding causality or stability constraints to the problems failed when it was realized that these time based concepts were undefined and; in fact, undefinable; in the Hilbert and Banach spaces of classical operator theory.