Hausdorff means and moment sequences

Positivity ◽  
2010 ◽  
Vol 15 (1) ◽  
pp. 17-48 ◽  
Author(s):  
Grahame Bennett
Keyword(s):  
Hausdorff Means

Hausdorff means and Gibbs phenomenon

1968 ◽  
Vol 107 (1) ◽  
pp. 21-32 ◽  
Author(s):  
Masako Izumi ◽  
Shin-ichi Izumi
Keyword(s):  
Gibbs Phenomenon ◽  
Hausdorff Means

scholarly journals On approximation in generalized Zygmund class

2019 ◽  
Vol 52 (1) ◽  
pp. 370-387
Author(s):  
Hare Krishna Nigam
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Conjugate Function ◽  
Degree Of Approximation ◽  
Zygmund Class ◽  
Conjugate Fourier Series ◽  
Product Method ◽  
Hausdorff Means

AbstractHere, we estimate the degree of approximation of a conjugate function {\tilde g} and a derived conjugate function {\tilde g'} , of a 2π-periodic function g \in Z_r^\lambda , r ≥ 1, using Hausdorff means of CFS (conjugate Fourier series) and CDFS (conjugate derived Fourier series) respectively. Our main theorems generalize four previously known results. Some important corollaries are also deduced from our main theorems. We also partially review the earlier work of the authors in respect of order of the Euler-Hausdorff product method.

An Inequality for Hausdorff Means

1943 ◽  
Vol s1-18 (1) ◽  
pp. 46-50 ◽  
Author(s):  
G. H. Hardy
Keyword(s):  
Hausdorff Means

The Hausdorff Means for Double Sequences

1967 ◽  
Vol 10 (3) ◽  
pp. 347-352 ◽  
Author(s):  
F. Ustina
Keyword(s):  
Basic Theory ◽  
Dimensional Case ◽  
Double Sequences ◽  
One Dimensional ◽  
The One ◽  
Hausdorff Means

The basic theory of the Hausdorff means for double sequences was developed some thirty - three years ago by C.R. Adams [1], and independently by F. Hallenbach [3], Yet today, many of the properties of these means remain largely uninvestigated. The calculations here, although clearly more complex, for the most part break down into obvious modifications of the calculations in the one dimensional case.

Convergence of the Hausdorff Means of Double Fourier Series*

1968 ◽  
Vol 11 (4) ◽  
pp. 585-591 ◽  
Author(s):  
Fred Ustina
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Double Fourier Series ◽  
Partial Sums ◽  
Closed Region ◽  
Hausdorff Means

In this paper we prove that if {sm, n(x, y)} is the sequence of partial sums of the Fourier series of a function f(x, y), which is periodic in each variable and of bounded variation in the sense of Hardy-Krause in the period rectangle, then {sm, n(x, y)} converges uniformly to f(x, y) in any closed region D in which this function is continuous at every point. This result is then used to prove that the regular Hausdorff means of the Fourier series of such a function also converge uniformly in such a region.

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