The absolute convergence of orthogonal series

1972 ◽  
Vol 12 (5) ◽  
pp. 743-746
Author(s):  
A. S. Zinov'ev
Keyword(s):  
Orthogonal Series ◽  
Absolute Convergence ◽  
The Absolute

scholarly journals On absolute generalized N"orlund summability of orthogonal series

2002 ◽  
Vol 33 (2) ◽  
pp. 161-166
Author(s):  
Y. Okuyama
Keyword(s):  
Orthogonal Series ◽  
General Theorem ◽  
Riesz Summability ◽  
Absolute Riesz Summability ◽  
The Absolute

In this paper, we shall prove a general theorem which contains two theorems on the absolute N"orlund summability and the absolute Riesz summability of orthogonal series.

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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