منابع مشابه
On Walsh-fourier Series^)
Every function f(x) which is of period 1 and Lebesgue integrable on [0, 1 ] may be expanded in a Walsh-Fourier series(3), f(x)~ ?.?=n ak\pk(x), where ak=fof(x)ypk(x)dx, k=0, 1, 2, • • • . Fine exhibited some of the basic similarities and differences between the trigonometric orthonormal system and the Walsh system. He identified the Walsh functions with the full set of characters of the dyadic ...
متن کاملSome criteria for determining when a Walsh Series is a Walsh-Fourier Series
We show that a general Walsh series is the Walsh-Fourier series of a function f ∈ Lp[0, 1] for 1 ≤ p <∞ if and only if its sequence of partial sums contains a relatively weakly compact subsequence. Several other criteria are established for the case where f ∈ LΦ[0, 1], the Orlicz space generated by an N -function Φ. Mathematics subject classification (2000): 42C10, 46E30
متن کاملStatistical Convergence of Walsh-fourier Series
This is a brief and concise account of the basic concepts and results on statistical convergence, strong Cesàro summability and Walsh-Fourier series. To emphasize the significance of statistical convergence, for example we mention the fact that the one-dimensional Walsh-Fourier series of an integrable (in Lebesgue’s sense) function may be divergent almost everywhere, but it is statistically con...
متن کاملConvergence of Trigonometric and Walsh - Fourier Series
In this paper we present some results on convergence and summability of oneand multi-dimensional trigonometric andWalsh-Fourier series. The Fejér and Cesàro summability methods are investigated. We will prove that the maximal operator of the summability means is bounded from the corresponding classical or martingale Hardy space Hp to Lp for some p > p0. For p = 1 we obtain a weak type inequalit...
متن کاملIntegral of Fine Computable functions and Walsh Fourier series
We define the effective integrability of Fine-computable functions and effectivize some fundamental limit theorems in the theory of Lebesgue integral such as Bounded Convergence Theorem and Dominated Convergence Theorem. It is also proved that the Walsh-Fourier coefficients of an effectively integrable Finecomputable function form an E-computable sequence of reals and converge effectively to ze...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1976
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1976-0410247-2