Smoothness conditions and Fourier series

DOI10.7153/mia-10-19zbMath1124.26002OpenAlexW2332871509MaRDI QIDQ3442288

Sergey Yu. Tikhonov

Publication date: 18 May 2007

Published in: Mathematical Inequalities & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/mia-10-19

zbMATH Keywords

trigonometric seriesLipschitz classmoduli of smoothness of fractional orderalmost increasing sequencealmost decreasing sequence

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Lipschitz (Hölder) classes (26A16) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Related Items (27)

Unnamed Item ⋮ Boas-type theorems for Laguerre type operator ⋮ Fourier-Bessel transforms and generalized uniform Lipschitz classes ⋮ Trigonometric series of Nikol'skii classes ⋮ Absolutely convergent Fourier-Bessel series and generalized Lipschitz classes ⋮ Mellin integral transforms and generalized Lipschitz and Zygmund spaces ⋮ Fourier cosine and sine transforms and generalized Lipschitz classes in the uniform metric ⋮ Multiple sine series and Nikol'skii classes in uniform metric ⋮ Boas and Titchmarsh type theorems for generalized Lipschitz classes and \(q\)-Bessel Fourier transform ⋮ Dual Boas type results for the quaternion transform and generalized Lipschitz spaces ⋮ Approximation of even functions with nonnegative Fourier coefficients by fractional Riesz sums ⋮ Absolutely convergent Fourier–Jacobi series and generalized Lipschitz classes ⋮ Boas-type results for Mellin transform ⋮ Dual Boas-type theorems and weighted integrability results for second Hankel-Clifford transform ⋮ Laguerre-Bessel transform and generalized Lipschitz classes ⋮ Boas type and Titchmarsh type theorems for generalized Fourier-Bessel transform ⋮ Generalized Lipschitz conditions for absolute convergence of weighted Jacobi-Dunkl series ⋮ Boas type results for two-sided quaternion Fourier transform and uniform Lipschitz spaces ⋮ Fourier transforms and fractional Lipschitz and Nikol'skii classes in uniform metric ⋮ Absolutely convergent \(q\)-Dunkl integrals and classical function spaces ⋮ Fourier transforms in generalized Lipschitz classes ⋮ Quaternion Fourier transform and generalized Lipschitz classes ⋮ Fourier transforms and generalized Lipschitz classes in uniform metric ⋮ Boas-type theorems for the \(q\)-Bessel Fourier transform ⋮ Boas-type theorems for the Bessel transform ⋮ Multiple Fourier coefficients and generalized Lipschitz classes in uniform metric ⋮ Fourier-Dunkl transforms and generalized symmetric Lipschitz classes

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