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AuthorKrabbe, Gregers. author
TitleOperational Calculus [electronic resource] / by Gregers Krabbe
ImprintBoston, MA : Springer US : Imprint: Springer, 1970
Connect tohttp://dx.doi.org/10.1007/978-1-4613-4392-9
Descript XVI, 349 p. 13 illus. online resource

SUMMARY

Since the publication of an article by G. DoETSCH in 1927 it has been known that the Laplace transform procedure is a reliable subยญ 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 unยญ 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)


Mathematics Science Mathematical analysis Analysis (Mathematics) Integral transforms Operational calculus Mathematics Analysis Integral Transforms Operational Calculus Science general



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