ISBN:
9781461343929
Language:
English
Pages:
Online-Ressource (XVI, 349 p)
,
online resource
Edition:
Springer eBook Collection. Humanities, Social Sciences and Law
Parallel Title:
Erscheint auch als
Parallel Title:
Erscheint auch als
Parallel Title:
Erscheint auch als
Keywords:
Science (General)
;
Mathematical analysis.
;
Social sciences.
;
Humanities.
Abstract:
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).
DOI:
10.1007/978-1-4613-4392-9
URL:
Volltext
(lizenzpflichtig)
Permalink
