
Operational Calculus
Gregers Krabbe(Author)
Springer (Publisher)
Published on 29. April 2012
Book
Paperback/Softback
XVI, 350 pages
978-3-642-87706-3 (ISBN)
Description
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).
More details
Edition
Softcover reprint of the original 1st ed. 1970
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
12 s/w Abbildungen
XVI, 350 p. 12 illus.
Dimensions
Height: 244 mm
Width: 170 mm
Thickness: 20 mm
Weight
635 gr
ISBN-13
978-3-642-87706-3 (9783642877063)
DOI
10.1007/978-3-642-87704-9
Schweitzer Classification
Other editions
Additional editions

Gregers Krabbe
Operational Calculus
Book
01/1970
Springer
€89.13
Article exhausted; check different version
Content
1.- §0. Operators.- § 1. Perfect Operators.- 2.- §2. The Basic Facts.- § 3. Elementary Applications.- § 4. Partial Fraction Decomposition.- 3.- §5. Further Applications.- § 6. Calculus of Operators.- §7. Vectors.- §8 Non-integrable Functions.- 4.- § 9. Partial Differential Equations.- § 10. Diffusion Problems.- 5.- § 11. Series of Operators.- § 12. A Functional Calculus for D.- § 13. Non-linear Equations.- § 14. Differential Equations with Polynomial Coefficients.- § 15. Theorems.- Three Basic Theorems.- A Theorem for § 6.- A Theorem for § 9.- A Theorem for § 11.- Glossary of Terminology and Notations.- Terminology.- Notations.- Summary of Results and Table of Formulas.- Elementary Formulas.- Periodic Functions.- Bibliographical Comments.- Subject and Author Index.