Degree of approximation of signals in certain Lipschitz classes by the Zweier–Euler product summability method of Fourier series

2020 ◽  
Author(s):  
Shilpa Das ◽  
Hemen Dutta
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Summability Method ◽  
Euler Product ◽  
Lipschitz Classes ◽  
Approximation Of Signals

scholarly journals Approximation of a Function Belonging to Lip ((α, r) Class by Np,q. C1 Summability Method of its Fourier Series

2014 ◽  
Vol 14 (2) ◽  
pp. 117-122 ◽  
Author(s):  
JP Kushwaha ◽  
BP Dhakal
Keyword(s):  
Fourier Series ◽  
Science And Technology ◽  
Degree Of Approximation ◽  
Summability Method ◽  
Approximation Of A Function

In this paper, an estimate for the degree of approximation of a function belonging to Lip(α, r) class by product summability method Np.q.C1 of its Fourier series has been established. DOI: http://dx.doi.org/10.3126/njst.v14i2.10424 Nepal Journal of Science and Technology Vol. 14, No. 2 (2013) 117-122

Trigonometric approximation of functions belonging to certain Lipschitz classes by C1 ⋅ T operator

2014 ◽  
Vol 07 (04) ◽  
pp. 1450064 ◽  
Author(s):  
Uaday Singh ◽  
Shailesh Kumar Srivastava
Keyword(s):  
Fourier Series ◽  
Trigonometric Polynomial ◽  
Degree Of Approximation ◽  
Approximation Properties ◽  
Periodic Functions ◽  
Lipschitz Classes ◽  
Matrix Means ◽  
Fir Digital Filters ◽  
Approximation Of Periodic Functions

The study of approximation properties of the periodic functions in Lp (p ≥ 1)-spaces, in general and in Lipschitz classes Lip α, Lip (α, p), Lip (ξ(t), p) and weighted Lipschitz class W(Lp, ω(t), β), in particular, through trigonometric Fourier series, although is an old problem and known as Fourier approximation in the existing literature, has been of a growing interests over the last four decades due to its application in filters and signals [E. Z. Psarakis and G. V. Moustakides, An L2-based method for the design of 1-D zero phase FIR digital filters, IEEE Trans. Circuits Systems I Fundam. Theory Appl., 44(7) (1997) 551–601]. The most common methods used for the determination of the degree of approximation of periodic functions are based on the minimization of the Lp-norm of f(x) - Tn(x), where Tn(x) is a trigonometric polynomial of degree n and called approximant of the function f. In this paper, we discuss the approximation properties of the periodic functions in the Lipschitz classes Lip α and W(Lp , ω(t), β), p ≥ 1 by a trigonometric polynomial generated by the product matrix means of the Fourier series associated with the function. The degree of approximation obtained in our theorems of this paper is free from p and sharper than earlier results.

scholarly journals On Approximation of Signals in the Generalized Zygmund Class Using (E,r)(N,qn) Mean of Conjugate Derived Fourier Series

2020 ◽  
Vol 13 (5) ◽  
pp. 1325-1336
Author(s):  
Anwesha Mishra ◽  
Birupakhya Prasad Padhy ◽  
Umakanta Misra
Keyword(s):  
Fourier Series ◽  
Present Article ◽  
Degree Of Approximation ◽  
Zygmund Class ◽  
Approximation Of Signals ◽  
Approximation Of Function

In the present article, we have established a result on degree of approximation of function in the generalized Zygmund class Zl(m),(l ≥ 1) by (E,r)(N,qn)- mean of conjugate derived Fourier series.

scholarly journals Approximation of signals by general matrix summability with effects of Gibbs Phenomenon

2019 ◽  
Vol 38 (6) ◽  
pp. 141-158 ◽  
Author(s):  
B. B. Jena ◽  
Lakshmi Narayan Mishra ◽  
S. K. Paikray ◽  
U. K. Misra
Keyword(s):  
Fourier Series ◽  
Gibbs Phenomenon ◽  
Degree Of Approximation ◽  
Trigonometric Polynomials ◽  
General Matrix ◽  
Matrix Summability ◽  
Partial Sum ◽  
Approximation Of Signals

In the proposed paper the degree of approximation of signals (functions) belonging to $Lip(\alpha,p_{n})$ class has been obtained using general sub-matrix summability and a new theorem is established that generalizes the results of Mittal and Singh [10] (see [M. L. Mittal and Mradul Veer Singh, Approximation of signals (functions) by trigonometric polynomials in $L_{p}$-norm, \textit{Int. J. Math. Math. Sci.,} \textbf{2014} (2014), ArticleID 267383, 1-6 ]). Furthermore, as regards to the convergence of Fourier series of the signals, the effect of the Gibbs Phenomenon has been presented with a comparison among different means that are generated from sub-matrix summability mean together with the partial sum of Fourier series of the signals.

scholarly journals Approximation of functions belonging to LIP (α, p) class by (E, 1)(N,pn) means of its fourier series

1970 ◽  
Vol 7 (1) ◽  
pp. 1-8
Author(s):  
Binod Prasad Dhakal
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Summability Method ◽  
Subject Classification ◽  
Approximation Of Functions ◽  
Keywords And Phrases ◽  
Approximation Of A Function

The present paper deals with approximation of a function belonging to the Lip (α, p) class by product summability method. Here product of Euler (E,1) summability method and Nörlund (N, pn) method has been taken. A new estimate on degree of approximation of a function f belonging to Lip (α, p) class has been determined by (E,1) (N, pn) summability of a Fourier series. Subject Classification: 40G05, 42B05, 42B08 Keywords and phrases: Degree of approximation; (E,1)(N, pn) summability; Fourier series; Lip (α, p) class; Lp norm.DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5416 KUSET 2011; 7(1): 1-8

scholarly journals On the approximation of function belonging to weighted $ {(L^p, \xi(t))}$ class by almost matrix summability method of its Fourier series

2004 ◽  
Vol 35 (1) ◽  
pp. 67-76 ◽  
Author(s):  
Shyam Lal
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Summability Method ◽  
Matrix Summability ◽  
Approximation Of Function

In this paper, the degree of approximation of function belonging to weighted $ W(L^p$, $ \xi(t))$ class by almost matrix summability of its Fourier series has been determined. The main theorem improves all the previously known theorems in this line of work.

scholarly journals On the degree of approximation of signals Lip(α,r), (r≥ 1) class by almost Riesz means of its Fourier series

2014 ◽  
pp. 79-87 ◽  
Author(s):  
Vishnu Narayan Mishra ◽  
Huzoor H. Khan ◽  
Idrees A. Khan ◽  
Lakshmi Narayan Mishra
Keyword(s):  
Fourier Series ◽  
Degree Of Approximation ◽  
Riesz Means ◽  
Approximation Of Signals
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