Arithmetic Functions, Convolution and Finite Fourier Series

2021 ◽  
pp. 73-97
Author(s):  
Vichian Laohakosol
Keyword(s):  
Fourier Series ◽  
Arithmetic Functions

scholarly journals Ramanujan-Fourier series of certain arithmetic functions of two variables

2017 ◽  
Vol Volume 39 ◽  
Author(s):  
Noboru Ushiroya
Keyword(s):  
Fourier Series ◽  
Pointwise Convergence ◽  
Sufficient Conditions ◽  
Arithmetic Functions ◽  
Functions Of Two Variables ◽  
International Audience ◽  
Series Of Functions

International audience We study Ramanujan-Fourier series of certain arithmetic functions of two variables. We generalize Delange's theorem to the case of arithmetic functions of two variables and give sufficient conditions for pointwise convergence of Ramanujan-Fourier series of arithmetic functions of two variables. We also give several examples which are not obtained by trivial generalizations of results on Ramanujan-Fourier series of functions of one variable.

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

The maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series

2008 ◽  
Vol 45 (3) ◽  
pp. 321-331
Author(s):  
István Blahota ◽  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Hardy Space ◽  
Maximal Operator ◽  
Fejér Means

In this paper we prove that the maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series is not bounded from the Hardy space H2/3 ( G2 ) to the space L2/3 ( G2 ).

Steady-state modelling method for matrix-reactance frequency converter with boost topology

2011 ◽  
Vol 60 (2) ◽  
pp. 137-148
Author(s):  
Igor Korotyeyev ◽  
Beata Zięba
Keyword(s):  
Fourier Series ◽  
Steady State ◽  
Differential Equations ◽  
Numerical Method ◽  
Frequency Converter ◽  
Double Fourier Series ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Modelling Method ◽  
Three Phase

Steady-state modelling method for matrix-reactance frequency converter with boost topologyThis paper presents a method intended for calculation of steady-state processes in AC/AC three-phase converters that are described by nonstationary periodical differential equations. The method is based on the extension of nonstationary differential equations and the use of Galerkin's method. The results of calculations are presented in the form of a double Fourier series. As an example, a three-phase matrix-reactance frequency converter (MRFC) with boost topology is considered and the results of computation are compared with a numerical method.

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