Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Overconvergence and $ (C,\,1)$ summability


Author: Vladimir Drobot
Journal: Proc. Amer. Math. Soc. 25 (1970), 13-15
MSC: Primary 30.21
DOI: https://doi.org/10.1090/S0002-9939-1970-0254220-0
MathSciNet review: 0254220
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that a power series can be diluted to become $ (C,1)$ summable outside the radius of convergence if and only if it overconverges.


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

  • [1] G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620
  • [2] S. Mazur, Conditionally convergent series, Soc. Sav. Sci. Lett. Lwow. 4 (1929), 411-424.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30.21

Retrieve articles in all journals with MSC: 30.21


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0254220-0
Keywords: Dilution of series, $ (C,1)$ summability, overconvergence of power series
Article copyright: © Copyright 1970 American Mathematical Society