Absolute Convergence. Bernstein and Peetre Theorems.

2017 ◽  
pp. 53-58
Author(s):  
Valery Serov
Keyword(s):  
Absolute Convergence

On the absolute convergence of multiple fourier series

2007 ◽  
Vol 117 (3) ◽  
pp. 275-292 ◽  
Author(s):  
Ferenc Móricz ◽  
Antal Veres
Keyword(s):  
Fourier Series ◽  
Absolute Convergence ◽  
Multiple Fourier Series ◽  
The Absolute

ON SETS OF ABSOLUTE CONVERGENCE

1981 ◽  
Vol 38 (2) ◽  
pp. 245-254
Author(s):  
R A Avetisjan
Keyword(s):  
Absolute Convergence

scholarly journals On the convergence criterion for branched continued fractions with independent variables

2018 ◽  
Vol 9 (2) ◽  
pp. 120-127 ◽  
Author(s):  
R.I. Dmytryshyn
Keyword(s):  
Power Series ◽  
Continued Fractions ◽  
Special Form ◽  
Absolute Convergence ◽  
Convergence Criterion ◽  
Complex Numbers ◽  
Independent Variables ◽  
Nonnegative Coefficients ◽  
Multiple Power ◽  
Multiple Power Series

In this paper, we consider the problem of convergence of an important type of multidimensional generalization of continued fractions, the branched continued fractions with independent variables. These fractions are an efficient apparatus for the approximation of multivariable functions, which are represented by multiple power series. We have established the effective criterion of absolute convergence of branched continued fractions of the special form in the case when the partial numerators are complex numbers and partial denominators are equal to one. This result is a multidimensional analog of the Worpitzky's criterion for continued fractions. We have investigated the polycircular domain of uniform convergence for multidimensional C-fractions with independent variables in the case of nonnegative coefficients of this fraction.

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