Mean approximation of periodic functions by Fourier series

1968 ◽  
pp. 101-125
Author(s):  
V. I. Berdyšev
Keyword(s):  
Fourier Series ◽  
Periodic Functions ◽  
Approximation Of Periodic Functions

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.

Approximation of periodic functions in certain sub-classes of Lp[0,2π]

2017 ◽  
Vol 10 (03) ◽  
pp. 1750046
Author(s):  
Uaday Singh ◽  
Soshal Saini
Keyword(s):  
Fourier Series ◽  
Trigonometric Approximation ◽  
Moduli Of Continuity ◽  
Periodic Functions ◽  
Matrix Means ◽  
Approximation Of Periodic Functions

In this paper, we determine the degree of trigonometric approximation of [Formula: see text]-periodic functions and their conjugates, in terms of the moduli of continuity associated with them, by matrix means of corresponding Fourier series. We also discuss some analogous results with remarks and corollaries.

Estimate of the approximation of periodic functions by Fourier series

2006 ◽  
Vol 79 (5-6) ◽  
pp. 726-728 ◽  
Author(s):  
O. V. Besov
Keyword(s):  
Fourier Series ◽  
Periodic Functions ◽  
Approximation Of Periodic Functions

On Strong Summability of Multiple Fourier Series and Approximation of Periodic Functions

1987 ◽  
Vol 133 (1) ◽  
pp. 211-236 ◽  
Author(s):  
Hans-Jürgen Schmeisser ◽  
Winfried Sickel
Keyword(s):  
Fourier Series ◽  
Multiple Fourier Series ◽  
Strong Summability ◽  
Periodic Functions ◽  
Approximation Of Periodic Functions

APPROXIMATION OF PERIODIC FUNCTIONS BY FEJÉR SUMS

1971 ◽  
Vol 5 (1) ◽  
pp. 86-96
Author(s):  
G K Lebed' ◽  
A A Avdeenko
Keyword(s):  
Periodic Functions ◽  
Approximation Of Periodic Functions
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