Estimates of Best Approximations of Transformed Fourier Series in Lp-Norm and p-Variational Norm

2020 ◽  
Vol 250 (3) ◽  
pp. 463-474
Author(s):  
S. S. Volosivets ◽  
A. A. Tyuleneva
Keyword(s):  
Fourier Series ◽  
Best Approximations ◽  
Lp Norm

Estimates of Functions with Transformed Double Fourier Series

2021 ◽  
Vol 58 (1) ◽  
pp. 32-83
Author(s):  
Boris V. Simonov
Keyword(s):  
Fourier Series ◽  
Double Fourier Series ◽  
Moduli Of Smoothness ◽  
Best Approximations

The paper provides a detailed study of inequalities of complete moduli of smoothness of functions with transformed Fourier series by moduli of smoothness of initial functions. Upper and lower estimates of the norms and best approximations of the functions with transformed Fourier series by the best approximations of initial functions are also obtained.

Convergence rate of fourier series and best approximations in the space Lp

1988 ◽  
Vol 39 (4) ◽  
pp. 389-398 ◽  
Author(s):  
A. I. Stepanets ◽  
A. K. Kushpel'
Keyword(s):  
Fourier Series ◽  
Convergence Rate ◽  
Best Approximations ◽  
The Space Lp

scholarly journals Partial best approximations and the absolute Cesaro summability of multiple Fourier series

2021 ◽  
Vol 103 (3) ◽  
pp. 4-12
Author(s):  
S. Bitimkhan ◽  
◽  
D.T. Alibieva ◽  
Keyword(s):  
Fourier Series ◽  
Sufficient Conditions ◽  
Multiple Fourier Series ◽  
Dimensional Case ◽  
Cesàro Summability ◽  
Best Approximations ◽  
One Dimensional ◽  
Cesaro Summability ◽  
The Absolute ◽  
The One

The article is devoted to the problem of absolute Cesaro summability of multiple trigonometric Fourier series. Taking a central place in the theory of Fourier series this problem was developed quite widely in the one-dimensional case and the fundamental results of this theory are set forth in the famous monographs by N.K. Bari, A. Zigmund, R. Edwards, B.S. Kashin and A.A. Saakyan [1–4]. In the case of multiple series, the corresponding theory is not so well developed. The multidimensional case has own specifics and the analogy with the one-dimensional case does not always be unambiguous and obvious. In this article, we obtain sufficient conditions for the absolute summability of multiple Fourier series of the function f ∈ Lq(Is) in terms of partial best approximations of this function. Four theorems are proved and four different sufficient conditions for the |C; β¯|λ-summability of the Fourier series of the function f are obtained. In the first theorem, a sufficient condition for the absolute |C; β¯|λ- summability of the Fourier series of the function f is obtained in terms of the partial best approximation of this function which consists of s conditions, in the case when β1 = ... = βs = 1/q'. Other sufficient conditions are obtained for double Fourier series. Sufficient conditions for the |C; β1; β2|λ-summability of the Fourier series of the function f ∈ Lq(I2) are obtained in the cases β1 = 1/q', −1 < β2 < 1/q'(in the second theorem), 1/q'< β1 < +∞, β2 = 1/q', (in the third theorem), −1 < β1 < 1/q', 1/q' < β2 < +∞ (in the fourth theorem).

Topology Optimization of IPM Motors using Fourier Series

2017 ◽  
Vol 137 (3) ◽  
pp. 245-253
Author(s):  
Hidenori Sasaki ◽  
Hajime Igarashi
Keyword(s):  
Fourier Series ◽  
Topology Optimization
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