A Wiener inversion-type theorem
James R. Holub
Proc. Amer. Math. Soc. 97 (1986), 399-402
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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.
R. Holub, On bases and the shift operator, Studia Math.
71 (1981/82), no. 2, 191–202. MR 654674
R. Holub, Shift basic sequences in the Wiener
disc algebra, Proc. Amer. Math. Soc.
88 (1983), no. 3,
699415 (84g:46075), http://dx.doi.org/10.1090/S0002-9939-1983-0699415-6
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
- J. Holub, On bases and the shift operator, Studia Math. 71 (1981), 191-202. MR 654674 (83f:47025)
- -, Shift basic sequences in the Wiener disc algebra, Proc. Amer. Math. Soc. 88 (1983), 464-468. MR 699415 (84g:46075)
- M. Naimark, Normed rings, Noordhoff, Groningen, 1964. MR 0355601 (50:8075)
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