On a problem of Gevorkyan for the Franklin system

Zygmunt Wronicz

doi:10.7494/opmath.2016.36.5.681

On a problem of Gevorkyan for the Franklin system

Opuscula Mathematica ◽

10.7494/opmath.2016.36.5.681 ◽

2016 ◽

Vol 36 (5) ◽

pp. 681 ◽

Cited By ~ 5

Author(s):

Zygmunt Wronicz

Keyword(s):

Franklin System

Download Full-text

Properties of the orthonormal Franklin system

Studia Mathematica ◽

10.4064/sm-23-2-141-157 ◽

1963 ◽

Vol 23 (2) ◽

pp. 141-157 ◽

Cited By ~ 68

Author(s):

Z. Ciesielski

Keyword(s):

Franklin System

Download Full-text

On a generalization of general Franklin system on R

Journal of Contemporary Mathematical Analysis ◽

10.3103/s1068362314060077 ◽

2014 ◽

Vol 49 (6) ◽

pp. 309-320 ◽

Cited By ~ 1

Author(s):

G. G. Gevorkyan ◽

K. A. Keryan

Keyword(s):

Franklin System ◽

General Franklin System

Download Full-text

ON A UNIQUENESS THEOREM FOR THE FRANKLIN SYSTEM

Proceedings of the YSU A: Physical and Mathematical Sciences ◽

10.46991/pysu:a/2018.52.2.093 ◽

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.

Download Full-text