scholarly journals Notes on Fourier analysis (XV): On the absolute convergence of trigonometrical series

1949 ◽  
Vol 1 (1) ◽  
pp. 46-49
Author(s):  
Shigeki Yano
Keyword(s):  
Fourier Analysis ◽  
Absolute Convergence ◽  
Trigonometrical Series ◽  
The Absolute

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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