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Uniform convergence of trigonometric series with general monotone coefficients

  • Mikhail Dyachenko,
    Department of Mechanics and Mathematics, Lomonosov Moscow State University, MSU, GSP-1, Moscow, 119991, Russia
  • Askhat Mukanov,
    Centre de Recerca Matemàtica and Universitat Autònoma de Barcelona, , Departament de Matematiques, Edifici C Facultat de Ciències , 08193 Bellaterra (Barcelona), Spain
  • Sergey Tikhonov,
    Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C 08193 Bellaterra (Barcelona), Spain
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Abstract

We study criteria for the uniform convergence of trigonometric series with general monotone coefficients. We also obtain necessary and sufficient conditions for a given rate of convergence of partial Fourier sums of such series.
Keywords: trigonometric series, general monotone sequence, uniform convergence trigonometric series, general monotone sequence, uniform convergence
MSC Classifications: 42A16, 42A20, 42A32 show english descriptions Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly 11F30}
Convergence and absolute convergence of Fourier and trigonometric series
Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
42A16 - Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly 11F30}
42A20 - Convergence and absolute convergence of Fourier and trigonometric series
42A32 - Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
 

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