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Абсолютная сходимос ть рядов Фурье—Хаара от суперпозиций функци й

Absolute convergence of Haar—Fourier series for superpositions of fnnctions

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Abstract

A necessary and sufficient condition is found for the functionφ to ensure absolute convergence of the Haar—Fourier series of all functionsφ(f) provided that the Haar—Fourier series off converges absolutely. Absolute convergence means absolute convergence of the series of coefficients, and the condition is thatφ should be in Lip 1.

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Литература

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  1. МЕХАН ИКО-МАТЕМАТИЧЕСКИЙ Ф АКУЛЬТЕТ, УНИВЕРСИТЕТ ИМЕНИ М. В. ЛОМОНОСОВА, МОСКО ВСКИЙ ГОСУДАРСТВЕНН ЫЙ, 117 234, МОСКВА, СССР

    П. Л. УЛЬЯНОВ

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  1. П. Л. УЛЬЯНОВ
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УЛЬЯНОВ, П.Л. Абсолютная сходимос ть рядов Фурье—Хаара от суперпозиций функци й. Analysis Mathematica 4, 225–236 (1978). https://doi.org/10.1007/BF01908991

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  • DOI: https://doi.org/10.1007/BF01908991

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