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Inversion of the Laplace Transform and Generation of Abel Summable Semigroups

โœ Scribed by Adam Bobrowski

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
182 KB
Volume
186
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

Necessary and sufficient conditions are given for a Banach-space-valued function f to be the Laplace-Stieltjes transform of a function of bounded variation. These conditions are used to obtain generation theorems for both absolutely continuous integrated semigroups and Abel summable semigroups.

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## Abstract We consider the problem of finding __u__ โˆˆ __L__ ^2^(__I__ ), __I__ = (0, 1), satisfying โˆซ~__I__~ __u__ (__x__ )__x__ d__x__ = __ฮผ__ ~__k__~ , where __k__ = 0, 1, 2, โ€ฆ, (__ฮฑ__ ~__k__~ ) is a sequence of distinct real numbers greater than โ€“1/2, and **__ฮผ__** = (__ฮผ__ ~__kl__~ ) is a g