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Operational Calculus

  • Book
  • © 1970

Overview

Authors:
  1. Gregers Krabbe

    1. Purdue University, USA

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-XVI
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  2. Chapter 1

    • Gregers Krabbe
    Pages 1-25

  3. Chapter 2

    • Gregers Krabbe
    Pages 26-83

  4. Chapter 3

    • Gregers Krabbe
    Pages 84-181

  5. Chapter 4

    • Gregers Krabbe
    Pages 182-241

  6. Chapter 5

    • Gregers Krabbe
    Pages 242-307

  7. Back Matter

    Pages 308-349
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Keywords

About this book

Since the publication of an article by G. DoETSCH in 1927 it has been known that the Laplace transform procedure is a reliable sub­ stitute for HEAVISIDE's operational calculus*. However, the Laplace transform procedure is unsatisfactory from several viewpoints (some of these will be mentioned in this preface); the most obvious defect: the procedure cannot be applied to functions of rapid growth (such as the 2 function tr-+-exp(t)). In 1949 JAN MIKUSINSKI indicated how the un­ necessary restrictions required by the Laplace transform can be avoided by a direct approach, thereby gaining in notational as well as conceptual simplicity; this approach is carefully described in MIKUSINSKI's textbook "Operational Calculus" [M 1]. The aims of the present book are the same as MIKUSINSKI's [M 1]: a direct approach requiring no un-necessary restrictions. The present operational calculus is essentially equivalent to the "calcul symbolique" of distributions having left-bounded support (see 6.52 below and pp. 171 to 180 of the textbook "Theorie des distributions" by LAURENT SCHWARTZ).

Authors and Affiliations

  • Purdue University, USA

    Gregers Krabbe

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