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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a problem of G. G. Lorentz regarding the norms of Fourier projections
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by Boris Shekhtman PDF
Proc. Amer. Math. Soc. 108 (1990), 187-190 Request permission

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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Additional Information
  • © Copyright 1990 American Mathematical Society
  • 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