Properties of general Fourier coefficients of differentiable functions
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Vakhtang Tsagareishvili
Abstract
The paper deals with problems of convergence of the series of moduli of the difference of general Fourier coefficients of functions from some differentiable class. It is shown that the good differentiable properties of a function do not guarantee the convergence of the series of moduli of the difference of general Fourier coefficients of this function. We explain the bounded variation of a sequence of general Fourier coefficients of a function from some functional class. We also find the conditions on the functions of an orthonormal system (ONS) under which the sequence of Fourier coefficients of any function from the differentiable class is of bounded variation. It is established that the resulting conditions are best possible. Studied here is the particular character of a subsequence of ONS.
References
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Articles in the same Issue
- Frontmatter
- On the Hölder continuity of ring Q-homeomorphisms
- New regularity results for the heat equation and application to non-homogeneous Burgers equation
- Maximum inequalities in rearrangements of orthogonal series
- A parallel type decomposition scheme for quasi-linear abstract hyperbolic equation
- Reversible ring property via idempotent elements
- Infinitely many solutions for perturbed Λγ-Laplace equations
- On an alternative approach for mixed boundary value problems for the Laplace equation
- Split monotone variational inclusion problem involving Cayley operators
- Duals and approximate duals of von Neumann–Schatten p-frames
- Properties of general Fourier coefficients of differentiable functions
- On linear spline algorithms of computerized tomography in the space of n-orbits
- Barbashin type characterizations for the uniform polynomial stability and instability of evolution families
