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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On a problem of G. G. Lorentz regarding the norms of Fourier projections


Author: Boris Shekhtman
Journal: Proc. Amer. Math. Soc. 108 (1990), 187-190
MSC: Primary 42A05; Secondary 42A45, 43A25
MathSciNet review: 994788
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Abstract: For any $ 0 < \alpha < \frac{1}{2}$ we construct a sequence of integers $ \left( {{\mu _1}, \ldots, {\mu _n}, \ldots } \right)$ such that the norms of Fourier projections

$\displaystyle {F_N} = \sum\limits_1^N {{e^{i{\mu _j}\theta }}} \otimes {e^{i{\m... ...}}}:{C_{\left[ { - \pi ,\pi } \right]}} \to {C_{\left[ { - \pi ,\pi } \right]}}$

grow as $ {N^\alpha }$ . This answers a question of Prof. G. G. Lorentz.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0994788-2
PII: S 0002-9939(1990)0994788-2
Article copyright: © Copyright 1990 American Mathematical Society