Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A characterization of $ B$-slowly varying functions


Author: Steven Bloom
Journal: Proc. Amer. Math. Soc. 54 (1976), 243-250
MathSciNet review: 0393375
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: A measurable function $ \varphi > 0$ that satisfies the limit condition $ {\lim _{x \to \infty }}(\varphi (x + t\varphi (x))/\varphi (x)) = 1$ for all $ t$ is said to be $ B$-slowly varying. If $ \varphi $ is continuous, this limit is shown to hold uniformly for $ t$ in compact sets, and an integral representation is derived.


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


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0393375-X
PII: S 0002-9939(1976)0393375-X
Article copyright: © Copyright 1976 American Mathematical Society