Multipliers for Walsh-Fourier series
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This article is published in Tohoku Mathematical Journal.The article was published on 1964-01-01 and is currently open access. It has received 33 citations till now. The article focuses on the topics: Fourier sine and cosine series & Sine and cosine transforms.read more
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Book
Analysis of Boolean Functions
TL;DR: This text gives a thorough overview of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry, and includes a "highlight application" such as Arrow's theorem from economics.
Journal ArticleDOI
Walsh-fourier series and the concept of a derivative †
Paul L. Butzer,H.J. Wagner +1 more
TL;DR: In this paper, a derivative of the Walsh-Fourier series on the dyadic group G has been defined, which has most properties in common with the ordinary derivative, and the fundamental theorem of the calculus is valid for these two notions, but no attempt has been made to define a derivative for functions f given on G.
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Martingale Morrey-Campanato Spaces and Fractional Integrals
Eiichi Nakai,Gaku Sadasue +1 more
TL;DR: In this article, the authors introduced the notion of martingale Morrey-Campanato spaces and established the boundedness of fractional integrals on these spaces, and showed that the maximal function of a fractional integral can be expressed as a transformation on the Martingale Lipschitz space.
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On dyadic analysis based on the pointwise dyadic derivative
Paul L. Butzer,H. J. Wagner +1 more
TL;DR: In this article, the authors proposed a method to improve the quality of the data collected by the data collection system by using the information gathered from the users' own data collection and the data gathered by the system itself.
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Fractional Integral on Martingale Hardy Spaces With Variable Exponents
Zhiwei Hao,Yong Jiao +1 more
TL;DR: In this paper, the authors investigated the boundedness of fractional integral operators on martingale Hardy spaces with variable exponents defined on a probability space and proved that Iαf, α > 0 is bounded under some reasonable assumptions.
References
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On Walsh-Fourier series
TL;DR: Theorem 5.1 Theorems on series of Walsh functions as discussed by the authors is a series of functions of period 1 and Lebesgue integrability on [0, 1 ] that may be expanded in a Walsh-Fourier series.
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On approximation by Walsh functions
TL;DR: In this paper, the authors define the Rademacher functions as a complete orthonormal set of the Walsh-Fourier series, and show that every periodic function integrable on (0, 1) will have associated with it a Walsh Fourier series.