Operational Calculus

1970
ISBN: 978-1-4613-4394-3
Verlag: Springer US

Buch, Englisch, 349 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 533 g

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).

Zielgruppe

Research

Autoren/Hrsg.

Krabbe, Gregors

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften Interdisziplinär
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen