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 t ~ 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 1J. . The aims of the present book are the same as MIKUSINSKI'S [M 1J: 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).
- ISBN10 3540048960
- ISBN13 9783540048961
- Publish Date 1 January 1970
- Publish Status Out of Print
- Out of Print 19 June 2015
- Publish Country DE
- Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
- Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Format Hardcover
- Pages 366
- Language English