scholarly journals Uniqueness of series in the Franklin system and the Gevorkyan problems

2021 ◽  
Vol 41 (2) ◽  
pp. 269
Author(s):  
Zygmunt Wronicz
Keyword(s):  
Franklin System

scholarly journals Properties of the orthonormal Franklin system

1963 ◽  
Vol 23 (2) ◽  
pp. 141-157 ◽  
Author(s):  
Z. Ciesielski
Keyword(s):  
Franklin System

On a generalization of general Franklin system on R

2014 ◽  
Vol 49 (6) ◽  
pp. 309-320 ◽  
Author(s):  
G. G. Gevorkyan ◽  
K. A. Keryan
Keyword(s):  
Franklin System ◽  
General Franklin System

ON A UNIQUENESS THEOREM FOR THE FRANKLIN SYSTEM

2018 ◽  
Vol 52 (2 (246)) ◽  
pp. 93-100
Author(s):  
K.A. Navasardyan
Keyword(s):  
Uniqueness Theorem ◽  
Partial Sums ◽  
Uniqueness Theorems ◽  
Franklin System ◽  
Almost Everywhere ◽  
Franklin Series

In this paper we prove that there exist a nontrivial Franklin series and a sequence $ M_n $ such that the partial sums $ S_{M_n} (x) $ of that series converge to 0 almost everywhere and $ \lambda \cdot \text{mes} \{ x : \sup\limits_{n}{\left| S_{M_n} (x) \right|} > \lambda \} \to 0 $ as $ \lambda \to +\infty $. This shows that the boundedness assumption of the ratio $ \dfrac{ M_{n+1}}{M_n} $, used for the proofs of uniqueness theorems in earlier papers, can not be omitted.

scholarly journals On a problem of Gevorkyan for the Franklin system

2016 ◽  
Vol 36 (5) ◽  
pp. 681 ◽  
Author(s):  
Zygmunt Wronicz
Keyword(s):  
Franklin System

On Uniqueness of Series by General Franklin System

2018 ◽  
Vol 53 (4) ◽  
pp. 223-231
Author(s):  
G. G. Gevorkyan ◽  
K. A. Navasardyan
Keyword(s):  
Franklin System ◽  
General Franklin System

Majorants and uniqueness of series in the Franklin system

1996 ◽  
Vol 59 (4) ◽  
pp. 373-391
Author(s):  
G. G. Gevorkyan
Keyword(s):  
Franklin System
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