In the paper, we give some results regarding the sufficient conditions for the absolute convergence of the Fourier series of a function using some of its axiomatic properties and constructive characteristics, such as the best approximation of the function with trigonometric polynomials, the modulus of continuity of the function, and the norm of the function in different spaces. Also, the sufficient conditions for the absolute convergence of the Fourier series of the convolution of two functions are provided.
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Rexhepi et al. (2024) studied this question.
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