Tauberian theorems for the Laplace-Stieltjes transform

Author:
C. J. K. Batty

Journal:
Trans. Amer. Math. Soc. **322** (1990), 783-804

MSC:
Primary 44A10; Secondary 30B50, 40E05, 47A60

MathSciNet review:
1013326

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Abstract: Let be a function of locally bounded variation, with , whose Laplace-Stieltjes transform is absolutely convergent for . Let be the singular set of in , and suppose that . Various estimates for are obtained. In particular, as if

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1990-1013326-6

Keywords:
Tauberian theorem,
Laplace-Stieltjes transform,
Laplace transform,
power series,
Dirichlet series,
-semigroup

Article copyright:
© Copyright 1990
American Mathematical Society