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)

 

On divergent lacunary trigonometric series


Author: L. Thomas Ramsey
Journal: Proc. Amer. Math. Soc. 90 (1984), 397-400
MSC: Primary 42A55; Secondary 28A12
MathSciNet review: 728355
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ S = \left\{ {{\lambda _n}} \right\}_{n = 1}^\infty $ be a sequence of positive real numbers such that $ {\lambda _{n + 1}}/{\lambda _n} \geqslant q > 1$ for all $ n$. If $ q > 8$ then any divergent series with frequencies in $ S$ has its real part diverging (uniformly) to $ + \infty $ on a set of positive logarithmic capacity. It is necessary that $ q > 2$. A new sufficient condition for the generalized capacity of a set to be positive is developed and then applied in the proof.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42A55, 28A12

Retrieve articles in all journals with MSC: 42A55, 28A12


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0728355-X
PII: S 0002-9939(1984)0728355-X
Keywords: Lacunary series, generalized capacity, logarithmic capacity
Article copyright: © Copyright 1984 American Mathematical Society