A uniqueness theorem for multiple Lacunary trigonometric series

1974 ◽  
Vol 16 (6) ◽  
pp. 1112-1115
Author(s):  
V. F. Gaposhkin
Keyword(s):  
Uniqueness Theorem ◽  
Trigonometric Series ◽  
Lacunary Trigonometric Series

scholarly journals The Riemann-Cantor uniqueness theorem for unilateral trigonometric series via a special version of the Lusin-Privalov theorem

2017 ◽  
Vol 71 (1) ◽  
pp. 73
Author(s):  
Raymond Mortini
Keyword(s):  
Uniqueness Theorem ◽  
Trigonometric Series ◽  
Simple Proof ◽  
Baire’S Theorem ◽  
Special Version

Using Baire's theorem, we give a very simple proof of a special version of the Lusin-Privalov theorem and deduce via Abel's  theorem the  Riemann-Cantor theorem on the uniqueness of the coefficients of pointwise convergent unilateral trigonometric series.

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