A Wiener inversion-type theorem

Author:
James R. Holub

Journal:
Proc. Amer. Math. Soc. **97** (1986), 399-402

MSC:
Primary 46J10

MathSciNet review:
840618

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Abstract: Let , a function in for which , and the operator of multiplication by on . It is shown that if and are integers for which and is the closed subspace of spanned by , then *is bounded below on* *does not have* *distinct zeros in any set of the form* , *where* *is a primitive* *th root of unity*.

**[1]**J. R. Holub,*On bases and the shift operator*, Studia Math.**71**(1981/82), no. 2, 191–202. MR**654674****[2]**J. R. Holub,*Shift basic sequences in the Wiener disc algebra*, Proc. Amer. Math. Soc.**88**(1983), no. 3, 464–468. MR**699415**, 10.1090/S0002-9939-1983-0699415-6**[3]**M. A. Naĭmark,*Normed rings*, Reprinting of the revised English edition, Wolters-Noordhoff Publishing, Groningen, 1970. Translated from the first Russian edition by Leo F. Boron. MR**0355601**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1986-0840618-8

Keywords:
Wiener disc algebra,
multiplication operator,
inversion theorem,
basic sequence,
shift basic sequence

Article copyright:
© Copyright 1986
American Mathematical Society