S. A. Telyakovskiĭ
Abstract
We present a necessary and sufficient condition for the series of absolute values of blocks of Fourier series elements and blocks of series of summands in Parseval’s identity to converge in the class of two-variable functions of bounded variation in the sense of Hardy.
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We present a necessary and sufficient condition for the series of absolute values of blocks of Fourier series elements and blocks of series of summands in Parseval’s identity to converge in the class of two-variable functions of bounded variation in the sense of Hardy.
Key concepts: Mathematics, Parseval's theorem, Function series, Fourier series, Series (stratigraphy), Bounded variation, Bounded function, Absolute convergence