On the Absolute Convergence of Fourier–Haar Series in the Metric of Lp(0, 1), 0 < p < 1

2019 ◽  
Vol 243 (6) ◽  
pp. 844-858
Author(s):  
M. G. Grigoryan
Keyword(s):  
Absolute Convergence ◽  
Haar Series ◽  
The Absolute

On the absolute convergence of Fourier series with respect to general orthonormal systems

2017 ◽  
Vol 24 (3) ◽  
pp. 471-478 ◽  
Author(s):  
Vakhtang Tsagareishvili
Keyword(s):  
Fourier Series ◽  
Absolute Convergence ◽  
Multiple Fourier Series ◽  
Haar Series ◽  
The Absolute

AbstractThe problems of absolute convergence of multiple Fourier series with respect to both general orthonormal systems and multiple Haar series are studied.

scholarly journals Continued Fractions with Absolutely Convergent Even or Odd Part

1959 ◽  
Vol 11 ◽  
pp. 131-140 ◽  
Author(s):  
David F. Dawson
Keyword(s):  
Continued Fractions ◽  
Continued Fraction ◽  
Absolute Convergence ◽  
The Absolute

The purpose of this paper is to give conditions under which the absolute convergence of the subsequence of odd or of even approximants to a continued fraction implies convergence of the continued fraction. In § 2 we consider the problem in general, and in § 3 we impose a condition which gives absolute convergence of the odd or of the even part of the continued fraction and state conditions which imply convergence of the continued fraction.

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