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＜電子ブック＞
Operational Calculus / by Gregors Krabbe

版	1st ed. 1970.
出版者	(New York, NY : Springer US : Imprint: Springer)
出版年	1970
本文言語	英語
大きさ	XVI, 349 p. 13 illus : online resource
著者標目	*Krabbe, Gregors author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Social sciences LCSH:Humanities FREE:Analysis FREE:Integral Transforms and Operational Calculus FREE:Humanities and Social Sciences
一般注記	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) HTTP:URL=https://doi.org/10.1007/978-1-4613-4392-9

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