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Operational Calculus

  • Gregers Krabbe

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Gregers Krabbe
    Pages 1-25
  3. Gregers Krabbe
    Pages 26-83
  4. Gregers Krabbe
    Pages 84-181
  5. Gregers Krabbe
    Pages 182-241
  6. Gregers Krabbe
    Pages 242-307
  7. Back Matter
    Pages 308-349

About this book

Introduction

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).

Keywords

calculus distribution growth operational calculus

Authors and affiliations

  • Gregers Krabbe
    • 1
  1. 1.Purdue UniversityUSA

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