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Research Papers
Continuous measures with large partial sums
A. Olofsson Division of Mathematics and Computer Science, Vrije Universiteit, Amsterdam, The Netherlands
Abstract:
It is proved that, in a weak sense, every measure in $M(\mathbb T)$ supported by a sufficiently singular Cantor set has asymptotically large Fourier partial sums. It is also shown that every measure in $M(\mathbb T)$ whose Fourier partial sums satisfy a mild growth condition has nontrivial null sets.
Keywords:
Dirichlet kernel, Lebesgue constants, Cantor sets.
Received: 26.02.2000
Citation:
A. Olofsson, “Continuous measures with large partial sums”, Algebra i Analiz, 13:3 (2001), 171–178; St. Petersburg Math. J., 13:3 (2002), 465–470
Linking options:
https://www.mathnet.ru/eng/aa942 https://www.mathnet.ru/eng/aa/v13/i3/p171
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