Classification of infinitely differentiable periodic functions

DOI10.1007/S11253-009-0185-1zbMath1199.26018OpenAlexW2024585450MaRDI QIDQ5325379

A. S. Serdyuk, A. I. Stepanets, Andrii Shidlich

Publication date: 8 August 2009

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-009-0185-1

zbMATH Keywords

entire functiontrigonometric polynomialinfinitely differentiable periodic functions\(2\pi\)-periodic functiongeneralized \(\bar\psi\)-derivative

Mathematics Subject Classification ID

Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Positive definite functions in one variable harmonic analysis (42A82)

Related Items (7)

Estimations of the best approximations for the classes of infinitely differentiable functions in uniform and integral metrics ⋮ Order estimates for the best approximations and approximations by Fourier sums in the classes of convolutions of periodic functions of low smoothness in the uniform metric ⋮ Asymptotic equalities for best approximations for classes of infinitely differentiable functions defined by the modulus of continuity ⋮ Uniform approximations by Fourier sums on the sets of convolutions of periodic functions of high smoothness ⋮ Jackson-type inequalities with generalized modulus of continuity and exact values of the \(n\)-widths for the classes of \((\psi,\beta)\)-differentiable functions in \(L_2\). I ⋮ Order Estimates of Best Orthogonal Trigonometric Approximations of Classes of Infinitely Differentiable Functions ⋮ Approximation by interpolation trigonometric polynomials in metrics of the space \(L_p\) on the classes of periodic entire functions

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