scholarly journals A uniform convergence criterion for non-harmonic sine series

2021 ◽  
Vol 212 (1) ◽  
Author(s):  
Kristina Artakovna Oganesyan
Keyword(s):  
Uniform Convergence ◽  
Convergence Criterion ◽  
Sine Series

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 Uniform convergence and everywhere convergence of Fourier series. II

1973 ◽  
Vol 9 (3) ◽  
pp. 337-342
Author(s):  
Masako Izumi ◽  
Shin-ichi Izumi
Keyword(s):  
Fourier Series ◽  
Uniform Convergence ◽  
Convergence Criterion ◽  
Convergent Fourier Series ◽  
Proper Generalization

The first theorem shows that the subspaces of the space of functions with everywhere convergent Fourier series, defined in our previous paper, is a good subspace. The second theorem shows that convergence criterion in the previous paper is the proper generalization of Lebesgue's Convergence Criterion.

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
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