منابع مشابه
Bounded Functions and Fourier Transforms
1. Statement of the principal result. The class of sequences obtainable as Fourier coefficients of measures on the circle group presents numerous structure problems of interest. Amongst the earliest results somewhat akin to that stated below appear Banach's theorems about lacunary coefficients; see e.g., [4, pp. 215-220]. More recently Helson [3] has studied analogous questions when the group c...
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Continued fraction expansions for the eigenvalues A= A(I', h2 ) and for the Fourier coefficients c~n/co are given by Tamir and Wang in [2]. These relations are valid both in the s table (I' real) and unstable (I' complex) regions . F (I') == C~,.1Co is numerically evaluated and depicted. It is seen from the graphs in [2] that the given formulas for C~,JCO are not particularly suitable for numer...
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A pseudo-Boolean function is a real-valued function defined on {0, 1}. A k-bounded function is a pseudo-Boolean function that can be expressed as a sum of subfunctions each of which depends on at most k input bits. The k-bounded functions for constant k play an important role in a number of research areas including molecular biology, biophysics, and evolutionary computation. In this paper, we c...
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A condition on the Walsh-Fourier coefficients of a continuous function/ sufficient to conclude that/is locally constant is obtained. The condition contains certain conditions identified earlier by Boikarev, Coury, Skvorcov and Wade, and Powell and Wade.
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In the first part of the paper we establish the pointwise convergence as t → +∞ for convolution operators ∫ Rd tdK (ty)φ(x− y)dy under the assumptions that φ(y) has integrable derivatives up to an order α and that |K(y)| ≤ c (1 + |y|)−β with α+β > d. We also estimate the Hausdorff dimension of the set where divergence may occur. In particular, when the kernel is the Fourier transform of a bound...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1941
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1941-07367-2