On the Rate of Convergence of Cesàro Means of Walsh-Fourier Series

Fridli, S.

doi:10.1006/jath.1994.1003

Cited by 25 publications

(9 citation statements)

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“…f for all integrable function f with constant sequence˛n D˛1 > 0. On the rate of convergence of Cesàro means in this constant case see the paper of Fridli [4]. For the two-dimensional situation see the paper of Goginava [7].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Convergence of Ces\'{a}ro means with varying parameters of Walsh-Fourier series

Joudeh¹,

Ahmad²

2018

MMN

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In 2007 Akhobadze [1] (see also [2]) introduced the notion of Cesàro means of Fourier series with variable parameters. In the present paper we prove the almost everywhere convergence of the the Cesàro .C;˛n/ means of integrable functions ˛n n f ! f , where N˛; K 3 n ! 1 for f 2 L 1 .I /, where I is the Walsh group for every sequence˛D .˛n/, 0 <˛n < 1. This theorem for constant sequences˛that is,˛Á˛1 was proved by Fine [3].

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Convergence of Ces\'{a}ro means with varying parameters of Walsh-Fourier series

Joudeh¹,

Ahmad²

2018

MMN

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“…Fridli [37] used dyadic modulus of continuity to characterize the set of functions in the space L p , whose Vilenkin-Fejér means converge at a given rate. It is also known that (see e.g books [2] and [116])…”

Section: January 31 2022mentioning

confidence: 99%

Bounded operators on Martingale Hardy spaces

Tutberidze¹

2022

Preprint

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The classical Fourier Analysis has been developed in an almost unbelieved way from the first fundamental discoveries by name Fourier. Especially a number of wonderful results have been proved and new directions of such research has been developed e.g. concerning Wavelets Theory, Gabor theory, Time-Frequency Analysis, Fast Fourier Transform, Abstract Harmonic Analysis, etc. One important reason for this is that this development is not only important for improving the "State of the art", but also for its importance in other areas of mathematics and also for several applications (e.g. theory of signal transmission, multiplexing, filtering, image enhancement, coding theory, digital signal processing and pattern recognition.)The classical theory of Fourier series deals with decomposition of a function into sinusoidal waves. Unlike these continuous waves the Vilenkin (Walsh) functions are rectangular waves. The development of the theory of Vilenkin-Fourier series has been strongly influenced by the classical theory of trigonometric series. Because of this it is inevitable to compare results of Vilenkin series to those on trigonometric series. There are many similarities between these theories, but there exist differences also. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group.

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“…convergence of the Walsh-Fejér means σ α n n ( f ) for all integrable function f with constant sequence α n = α > 0 is due to Fine [4] (see also Weisz [17]). On the rate of convergence of Cesà ro means in this constant case, see the paper of Yano [19], Fridli [5]. Approximation properties of Cesàro means of negative order with constant sequence were investigated by the second author [8].…”

Section: Introductionmentioning

confidence: 99%