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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
DOI: https://doi.org/10.1090/S0002-9939-1990-0994788-2
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 \[ {F_N} = \sum \limits _1^N {{e^{i{\mu _j}\theta }}} \otimes {e^{i{\mu _{{j^t}}}}}:{C_{\left [ { - \pi ,\pi } \right ]}} \to {C_{\left [ { - \pi ,\pi } \right ]}}\] grow as ${N^\alpha }$ . This answers a question of Prof. G. G. Lorentz.


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Article copyright: © Copyright 1990 American Mathematical Society