scholarly journals On the uniform convergence of double sine series

2009 ◽  
Vol 193 (1) ◽  
pp. 79-97 ◽  
Author(s):  
Péter Kórus ◽  
Ferenc Móricz
Keyword(s):  
Uniform Convergence ◽  
Sine Series

scholarly journals On the Uniform Convergence of Sine Series with Square Root

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Sergiusz Kęska
Keyword(s):  
Uniform Convergence ◽  
Real Sequence ◽  
Sufficient Condition ◽  
Square Root ◽  
Necessary And Sufficient Condition ◽  
Sine Series ◽  
Convergence Of Series ◽  
Necessary And Sufficient

Chaundy and Jolliffe proved that if {ck}k=1∞ is a nonincreasing real sequence with limk→∞ck=0, then the series ∑k=1∞‍cksin⁡kx converges uniformly if and only if kck→0. The purpose of this paper is to show that kck→0 is a necessary and sufficient condition for the uniform convergence of series ∑k=1∞‍cksin⁡kθ in θ∈[0,π]. However for ∑k=1∞‍cksin⁡k2θ it is not true in θ∈[0,π].

scholarly journals On the uniform convergence of double sine series

2018 ◽  
Vol 151 (1) ◽  
pp. 71-95 ◽  
Author(s):  
Krzysztof Duzinkiewicz ◽  
Bogdan Szal
Keyword(s):  
Uniform Convergence ◽  
Sine Series
Sign in / Sign up

Export Citation Format

Share Document