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Proceedings of the American Mathematical Society

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

 

 

On nonstrongly regular matrices


Authors: J. Bazinet and J. A. Siddiqi
Journal: Proc. Amer. Math. Soc. 34 (1972), 428-432
MSC: Primary 40C05
DOI: https://doi.org/10.1090/S0002-9939-1972-0294935-3
MathSciNet review: 0294935
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Abstract: Using the Rudin-Shapiro sequence, the existence of a regular but not strongly regular positive matrix that sums $ \{ \exp (2\pi ikt)\} $ to 0 for all $ t \in (0,1)$ is established. As a corollary it is shown that there exist matrices that sum all almost periodic sequences without possessing the Borel property and vice versa.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0294935-3
Keywords: Regular, strongly regular, almost convergence, Fourier-effective, Borel property, almost periodic
Article copyright: © Copyright 1972 American Mathematical Society