Convergence and Summability of Trigonometric Fourier Series and Their Conjugates in the Spaces $$L^p \left( T \right),p \in \left] {0, + \infty } \right[$$

1996 ◽  
pp. 71-92
Author(s):  
Levan Zhizhiashvili
Keyword(s):  
Fourier Series ◽  
Trigonometric Fourier Series

scholarly journals The multipliers of multiple trigonometric Fourier series

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Aizhan Ydyrys ◽  
Lyazzat Sarybekova ◽  
Nazerke Tleukhanova
Keyword(s):  
Fourier Series ◽  
Sufficient Conditions ◽  
Regular System ◽  
Multiple Fourier Series ◽  
Trigonometric Fourier Series ◽  
Lorentz Spaces ◽  
Complex Numbers ◽  
Multiple Trigonometric Fourier Series

Abstract We study the multipliers of multiple Fourier series for a regular system on anisotropic Lorentz spaces. In particular, the sufficient conditions for a sequence of complex numbers {λk}k∈Zn in order to make it a multiplier of multiple trigonometric Fourier series from Lp[0; 1]n to Lq[0; 1]n , p > q. These conditions include conditions Lizorkin theorem on multipliers.

Multiscale Modeling of Random Lattices: Critical Issues on Continuum Approximation

2011 ◽  
Author(s):  
Haifeng Zhao ◽  
Gregory J. Rodin
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Multiscale Modeling ◽  
Trigonometric Fourier Series ◽  
Continuum Approximation ◽  
Various Boundary Conditions ◽  
Random Lattices ◽  
Critical Issues

In this work, we are concerned that transmission of various boundary conditions through irregular lattices. The boundary conditions are parameterized using trigonometric Fourier series, and it is shown that, under certain conditions, transmission through irregular lattices can be well approximated by that through classical continuum. It is determined that such transmission must involve the wavelength of at least 12 lattice spacings; for smaller wavelength classical continuum approximations become increasingly inaccurate.

Functions of Minimal Norm with the Given Set of Fourier Coefficients

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 651
Author(s):  
Pyotr Ivanshin
Keyword(s):  
Fourier Series ◽  
Existence And Uniqueness ◽  
Fourier Coefficients ◽  
Nonnegative Function ◽  
Trigonometric Fourier Series ◽  
Minimum Norm ◽  
Minimal Norm ◽  
Uniqueness Of The Solution ◽  
The Given

We prove the existence and uniqueness of the solution of the problem of the minimum norm function ∥ · ∥ ∞ with a given set of initial coefficients of the trigonometric Fourier series c j , j = 0 , 1 , … , 2 n . Then, we prove the existence and uniqueness of the solution of the nonnegative function problem with a given set of coefficients of the trigonometric Fourier series c j , j = 1 , … , 2 n for the norm ∥ · ∥ 1 .

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