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Transactions of the American Mathematical Society

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A characterization of the complemented translation-invariant subspaces of $ H\sp 1({\bf R})$


Author: Dale E. Alspach
Journal: Trans. Amer. Math. Soc. 323 (1991), 197-207
MSC: Primary 43A15; Secondary 46J15
DOI: https://doi.org/10.1090/S0002-9947-1991-0986683-5
MathSciNet review: 986683
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Abstract: The purpose of this paper is to characterize the complemented translation-invariant subspaces of $ {H^1}({\mathbf{R}})$ in terms of the zero set of the Fourier transform. It is shown that if $ X$ is such a subspace then $ X = I(A)$ where $ A$ is in the ring generated by arithmetic progressions and lacunary sequences and $ A$ is $ \varepsilon$-separated for some $ \varepsilon > 0$. This proves a conjecture of the author and D. Ullrich.


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DOI: https://doi.org/10.1090/S0002-9947-1991-0986683-5
Article copyright: © Copyright 1991 American Mathematical Society