General orthonormal systems and absolute convergence

DOI10.1070/IM8862zbMath1458.42003OpenAlexW2996024675MaRDI QIDQ5118073

Vakhtang Tsagareishvili

Publication date: 4 September 2020

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/im8862

zbMATH Keywords

function of bounded variationFourier coefficientsorthonormal systemabsolute convergence of Fourier series

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Convergence and absolute convergence of Fourier and trigonometric series (42A20) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Related Items (7)

Differentiable functions and their Fourier coefficients ⋮ Smooth functions and general Fourier coefficients ⋮ Problems of unconditional convergence ⋮ The variation of general Fourier coefficients ⋮ Convergence of general Fourier series of differentiable functions ⋮ Properties of general Fourier coefficients of differentiable functions ⋮ The variation of general Fourier coefficients of Lipschitz class functions

Cites Work

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• On the structure of the class \(A(\varphi )\)
• Fourier coefficients of continuous functions
• Integrated orthonormal series
• Absolute convergence of Fourier series of functions of class $ \operatorname{Lip}1$ and of functions of bounded variation
• On Fourier coefficients of functions with respect to general orthonormal systems
• ABSOLUTE CONVERGENCE OF FOURIER SERIES WITH RESPECT TO COMPLETE ORTHONORMAL SYSTEMS

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