Operational Calculus

krabbe , gregers

ISBN 10: 3540048960 / ISBN 13: 9783540048961

Published by Springer Verlag, 1970

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Bibliographic Details

• Title: Operational Calculus
• Publisher: Springer Verlag
• Publication Date: 1970
• Language: English
• ISBN 10: 3540048960
• ISBN 13: 9783540048961
• Binding: hardcover
• Condition: Acceptable

About this title

Synopsis

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).