Abstract
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.
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