Operational Calculus (eBook)

Gregors Krabbe (Autor)

eBook Download: PDF

2013
Springer US (Verlag)
9781461343929 (ISBN)

Infos

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 "e;Operational Calculus"e; [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 "e;calcul symbolique"e; of distributions having left-bounded support (see 6.52 below and pp. 171 to 180 of the textbook "e;Theorie des distributions"e; by LAURENT SCHWARTZ).

Produkt-Details

• Erscheint lt. Verlag: 1.12.2013
• Sprache: englisch
• Themenwelt: Sonstiges ► Geschenkbücher
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Sozialwissenschaften
• ISBN-13: 9781461343929 / 9781461343929