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)

 

Shift basic sequences in the Wiener disc algebra


Author: J. R. Holub
Journal: Proc. Amer. Math. Soc. 88 (1983), 464-468
MSC: Primary 46J15; Secondary 46E15, 47B37
MathSciNet review: 699415
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ W(D)$ denote the set of functions $ f(z) = \sum\nolimits_{n = 0}^\infty {{a_n}{z^n}} $ for which $ \sum\nolimits_{n = 0}^\infty {\left\vert {{a_n}} \right\vert < + \infty } $. It is shown that for any positive integer $ k$ the $ k$-shifted sequence $ \left\{ {{z^{kn}} \cdot f(z)} \right\}_{n = 0}^\infty $ is a basic sequence in $ W(D)$ equivalent to the basis $ \left\{ {{z^n}} \right\}_{n = 0}^\infty $ if and only if $ f(z)$ has no set of $ k$ symmetrically distributed zeros on the circle $ \left\vert z \right\vert = 1$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46J15, 46E15, 47B37

Retrieve articles in all journals with MSC: 46J15, 46E15, 47B37


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0699415-6
PII: S 0002-9939(1983)0699415-6
Keywords: Wiener algebra, basis, basic sequence, shift operator
Article copyright: © Copyright 1983 American Mathematical Society