On an infinite linear combination of partial sums of Fourier series
نویسندگان
چکیده
منابع مشابه
Exponential Approximations Using Fourier Series Partial Sums
The problem of accurately reconstructing a piece-wise smooth, 2π-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f an...
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uniformly in x as h—»0, we shall say briefly that/ belongs to Lip a. Following 4](1)) we shall say that/ belongs to a) uniformly as *—>0. a notation already used (see Zygmund lipa, 0<a<l, if \f(x+h)-f(x)\=o(\h It is a classical result of Lebesgue (see Zygmund [5, p. 61 ] ; hereafter this book will be denoted by T.S.) that if / belongs to Lip a and if sn denotes the nth partial sum of the Fourie...
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چکیده ندارد.
15 صفحه اولA Note on the Fourier Coefficients and Partial Sums of Vilenkin-fourier Series
The aim of this paper is to investigate Paley type and HardyLittlewood type inequalities and strong convergence theorem of partial sums of Vilenkin-Fourier series. Let N+ denote the set of the positive integers, N := N+ ∪ {0}. Let m := (m0,m1, . . .) denote a sequence of the positive numbers, not less than 2. Denote by Zmk := {0, 1, . . . ,mk − 1} the additive group of integers modulomk. Define...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1976
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-56-2-93-100