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Uniqueness of Trigonometric Series
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) ( IF 0.3 ) Pub Date : 2020-12-28 , DOI: 10.3103/s1068362320060059 G. G. Gevorkyan
中文翻译:
三角级数的唯一性
更新日期:2020-12-28
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) ( IF 0.3 ) Pub Date : 2020-12-28 , DOI: 10.3103/s1068362320060059 G. G. Gevorkyan
Abstract
It is proven that, if the Riemann sums of a trigonometric series are bounded everywhere, perhaps, except for some countable set and converge in measure to a bounded function \(f\), then this series is the Fourier series of the function \(f\). This implies the generalizations of the Cantor and Young theorems.
中文翻译:
三角级数的唯一性
摘要
证明了,如果一个三角级数的黎曼和总有界,也许除了有一些可数集并在一定程度上收敛到有界函数\(f \),那么这个级数就是函数\(的傅立叶级数f \)。这意味着Cantor和Young定理的推广。