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Uniqueness for Trigonometric Series
The Annals of Mathematics, 1987A question going back to N. K. Bary in 1923 asked for conditions on a sequence \((a_n)\) which would ensure that, if \(\sum_{| n| \leq N}a_ ne^{int}\to 0\) a.e. as \(N\to \infty\), then \(a_n=0\) for all \(n\). A sufficient condition, for example (following from Carleson's Theorem but also susceptible to a more elementary proof), is that \(\sum^{\infty}
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ON THE SUMS OF TRIGONOMETRIC SERIES
Russian Mathematical Surveys, 1980Contents § 1. Introduction § 2. Subsidiary material § 3. Elementary facts about the sums of certain series § 4. Differentiability properties § 5. On bounds, intervals of constant sign, and roots of sums of sine-series § 6. Intervals of constant sign and estimates of sums of cosine-series § 7. On monotonicity of sums of sine- and cosine-series § 8.
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2003
Professor Zygmund's Trigonometric Series, first published in Warsaw in 1935, established itself as a classic. It presented a concise account of the main results then known, but was on a scale which limited the amount of detailed discussion possible. A greatly enlarged second edition published by Cambridge in two volumes in 1959 took full account of ...
A. Zygmund, Robert Fefferman
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Professor Zygmund's Trigonometric Series, first published in Warsaw in 1935, established itself as a classic. It presented a concise account of the main results then known, but was on a scale which limited the amount of detailed discussion possible. A greatly enlarged second edition published by Cambridge in two volumes in 1959 took full account of ...
A. Zygmund, Robert Fefferman
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On the Summability of Trigonometrical Series
Journal of the London Mathematical Society, 1932openaire +1 more source
Refinements of Wilker–Huygens-Type Inequalities via Trigonometric Series
Symmetry, 2021Gabriel Bercu
exaly
Trigonometric series with general monotone coefficients
Journal of Mathematical Analysis and Applications, 2007Sergey Tikhonov
exaly