Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \alpha :[0,\infty ) \to {\mathbf{C}}$ be a function of locally bounded variation, with $ \alpha (0) = 0$, whose Laplace-Stieltjes transform $ g(z) = \int_0^\infty {{e^{ - zt}}d\alpha (t)} $ is absolutely convergent for $ \operatorname{Re} z > 0$. Let $ E$ be the singular set of $ g$ in $ i{\mathbf{R}}$, and suppose that $ 0 \notin E$. Various estimates for $ \lim {\sup _{t \to \infty }}\vert\alpha (t) - g(0)\vert$ are obtained. In particular, $ \alpha (t) \to g(0)$ as $ t \to \infty $ if

\begin{displaymath}\begin{gathered}({\text{i)}}\quad E\,{\text{is null,}} \hfill... ...vert\alpha (s) - \alpha (t)\vert = 0. \hfill \\ \end{gathered} \end{displaymath}

This result contains Tauberian theorems for Laplace transforms, power series, and Dirichlet series.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 44A10, 30B50, 40E05, 47A60

Retrieve articles in all journals with MSC: 44A10, 30B50, 40E05, 47A60

Additional Information

PII: S 0002-9947(1990)1013326-6
Keywords: Tauberian theorem, Laplace-Stieltjes transform, Laplace transform, power series, Dirichlet series, $ {C_0}$-semigroup
Article copyright: © Copyright 1990 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia