Degree of Approximation of Conjugate Fourier Series of Functions in Besov space by Riesz Mean

2021 ◽  
Vol 67 (6) ◽  
pp. 145-166
Author(s):  
Madhusmita Mohanty ◽  
Sanghamitra Beuria
Keyword(s):  
Fourier Series ◽  
Besov Space ◽  
Degree Of Approximation ◽  
Conjugate Fourier Series ◽  
Riesz Mean ◽  
Series Of Functions

Degree of approximation of Fourier series of functions in Besov space by deferred Nörlund mean

2021 ◽  
pp. 2250033
Author(s):  
Birupakhya Prasad Padhy ◽  
Laxmipriya Nayak
Keyword(s):  
Fourier Series ◽  
Rate Of Convergence ◽  
Besov Space ◽  
Degree Of Approximation ◽  
Series Of Functions

In the present paper, we estimate the rate of convergence of Fourier series of functions by Deferred Nörlund mean in Besov space which is a generalization of [Formula: see text] space.

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.

scholarly journals Best approximation of conjugate of a function in generalized Zygmund

2019 ◽  
Vol 50 (4) ◽  
pp. 417-427
Author(s):  
Hare Krishna Nigam
Keyword(s):  
Fourier Series ◽  
Error Estimates ◽  
Best Approximation ◽  
Degree Of Approximation ◽  
Time Study ◽  
Zygmund Class ◽  
Conjugate Fourier Series ◽  
First Time

In this paper, we, for the very first time, study the error estimates of conjugate of a function ~g of g(2-periodic) in generalized Zygmund class Y wz (z 1); by Matix-Euler (TEq) product operatorof conjugate Fourier series. In fact, we establish two theorems on degree of approximation of afunction ~g of g (2-periodic) in generalized Zygmund class Y wz (z 1); by Matix-Euler (TEq)product means of its conjugate Fourier series. Our main theorem generalizes three previouslyknown results. Thus the results of [7], [8] and [26] become the particular cases of our Theorem2.1. Some corollaries are also deduced from our main theorem.

scholarly journals Degree of approximation of conjugate of a function belonging toLip(ξ(t),p)class by matrix summability means of conjugate Fourier series

2001 ◽  
Vol 27 (9) ◽  
pp. 555-563 ◽  
Author(s):  
Shyam Lal ◽  
Hare Krishna Nigam
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Conjugate Series ◽  
Conjugate Fourier Series ◽  
Matrix Summability

We determine the degree of approximation of conjugate of a function belonging toLip(ξ(t),p)class by matrix summability means of a conjugate series of a Fourier series.

scholarly journals The degree of approximation by Hausdorff means of a conjugate Fourier series

2016 ◽  
Vol 70 (2) ◽  
pp. 63
Author(s):  
Sergiusz Kęska
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Lipschitz Class ◽  
Conjugate Series ◽  
Conjugate Fourier Series ◽  
Hausdorff Means ◽  
Approximation Of A Function

The purpose of this paper is to analyze the degree of approximation of a function \(\overline f\) that is a conjugate of a function \(f\) belonging to the Lipschitz class by Hausdorff means of a conjugate series of the Fourier series.

A SUMMABILITY METHOD FOR FOURIER SERIES OF FUNCTIONS OF GENERALIZED BOUNDED VARIATION

Analysis ◽  
1997 ◽  
Vol 17 (2-3) ◽  
pp. 287-300
Author(s):  
LAWRENCE A. D'ANTONIO ◽  
DANIEL WATERMAN
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Summability Method ◽  
Series Of Functions
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