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Resolution Space, Operators and Systems

  • Book
  • © 1973

Overview

Authors:
  1. R. Saeks

    1. Dept. of Electrical Engineering, University of Notre Dame, Notre Dame, USA

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Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 82)

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-X
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  2. Causality

    • R. Saeks
    Pages 1-60

  3. Feedback Systems

    • R. Saeks
    Pages 61-113

  4. Dynamical Systems

    • R. Saeks
    Pages 114-154

  5. Time Invariance

    • R. Saeks
    Pages 155-203

  6. Back Matter

    Pages 204-270
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Keywords

About this book

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.

Authors and Affiliations

  • Dept. of Electrical Engineering, University of Notre Dame, Notre Dame, USA

    R. Saeks

Bibliographic Information

  • Book Title: Resolution Space, Operators and Systems

  • Authors: R. Saeks

  • Series Title: Lecture Notes in Economics and Mathematical Systems

  • DOI: https://doi.org/10.1007/978-3-642-80735-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin ยท Heidelberg 1973

  • Softcover ISBN: 978-3-540-06155-7Published: 05 February 1973

  • eBook ISBN: 978-3-642-80735-0Published: 06 December 2012

  • Series ISSN: 0075-8442

  • Series E-ISSN: 2196-9957

  • Edition Number: 1

  • Number of Pages: X, 270

  • Topics: Computer Science, general

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