scholarly journals Pointwise convergence of cone-like restricted two-dimensional (C,1) means of trigonometric Fourier series

2007 ◽  
Vol 149 (1) ◽  
pp. 74-102 ◽  
Author(s):  
György Gát
Keyword(s):  
Fourier Series ◽  
Pointwise Convergence ◽  
Trigonometric Fourier Series ◽  
Two Dimensional

Pointwise convergence of Marcinkiewicz-Fejér means of two-dimensional Walsh-Fourier series

2012 ◽  
Vol 49 (2) ◽  
pp. 236-253
Author(s):  
Ushangi Goginava ◽  
Ferenc Weisz
Keyword(s):  
Fourier Series ◽  
Pointwise Convergence ◽  
Two Dimensional ◽  
Fejér Means

In this paper we characterize the set of convergence of the Marcinkiewicz-Fejér means of two-dimensional Walsh-Fourier series.

scholarly journals Convergence and divergence of Fejér means of Fourier series on one and two-dimensional Walsh and Vilenkin groups

2008 ◽  
Vol 21 (3) ◽  
pp. 291-307
Author(s):  
György Gát
Keyword(s):  
Fourier Series ◽  
Harmonic Analysis ◽  
Pointwise Convergence ◽  
Point Of View ◽  
Two Dimensional ◽  
Fejér Means ◽  
Vilenkin Groups ◽  
Recent Developments ◽  
Convergence And Divergence

It is a highly celebrated issue in dyadic harmonic analysis the pointwise convergence of the Fej?r (or (C, 1)) means of functions on the Walsh and Vilenkin groups both in the point of view of one and two dimensional cases. We give a resume of the very recent developments concerning this matter, propose unsolved problems and throw a glance at the investigation of Vilenkin-like systems too. .

scholarly journals A note on the strong summability of two-dimensional Walsh–Fourier series

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
George Tephnadze
Keyword(s):  
Fourier Series ◽  
Strong Convergence ◽  
Studia Math ◽  
Trigonometric Fourier Series ◽  
Strong Summability ◽  
Two Dimensional ◽  
Convergence Theorems ◽  
Two Parameter

AbstractIn this paper, we investigate the strong summability of two-dimensional Walsh–Fourier series obtained in [F. Weisz, Strong convergence theorems for two-parameter Walsh–Fourier and trigonometric-Fourier series, Studia Math. 117 1996, 2, 173–194] (see Theorem W) and prove the sharpness of this result.

An analytical solution of a two-dimensional temperature field in a hollow cylinder under a time periodic boundary condition using Fourier series

2009 ◽  
Vol 223 (8) ◽  
pp. 1889-1901 ◽  
Author(s):  
G Atefi ◽  
M A Abdous ◽  
A Ganjehkaviri ◽  
N Moalemi
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Fourier Series ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Hollow Cylinder ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Separation Of Variables ◽  
Two Dimensional

The objective of this article is to derive an analytical solution for a two-dimensional temperature field in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface, while the inner surface is insulated. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel's theorem is used to solve the problem for a periodic boundary condition. The periodic boundary condition is decomposed using the Fourier series. This condition is simulated with harmonic oscillation; however, there are some differences with the real situation. To solve this problem, first of all the boundary condition is assumed to be steady. By applying the method of separation of variables, the temperature distribution in a hollow cylinder can be obtained. Then, the boundary condition is assumed to be transient. In both these cases, the solutions are separately calculated. By using Duhamel's theorem, the temperature distribution field in a hollow cylinder is obtained. The final result is plotted with respect to the Biot and Fourier numbers. There is good agreement between the results of the proposed method and those reported by others for this geometry under a simple harmonic boundary condition.

Sign in / Sign up

Export Citation Format

Share Document