TY  - JOUR
ID  - Wronicz2016
LB  - Wronicz2016
AU  - Wronicz, Zygmunt
TI  - On a problem of Gevorkyan for the Franklin system
ST  - On a problem of Gevorkyan for the Franklin system
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2016
VL  - 36
IS  - 5
SP  - 681
EP  - 687
DO  - http://dx.doi.org/10.7494/OpMath.2016.36.5.681
UR  - http://dx.doi.org/10.7494/OpMath.2016.36.5.681
AB  - In 1870 G. Cantor proved that if \(\lim_{N\rightarrow\infty}\sum_{n=-N}^N\,c_{n}e^{inx} = 0\) for every real \(x\), where \(\bar{c}_{n}=c_{n}\) (\(n\in \mathbb{Z}\)), then all coefficients \(c_{n}\) are equal to zero. Later, in 1950 V. Ya. Kozlov proved that there exists a trigonometric series for which a subsequence of its partial sums converges to zero, where not all coefficients of the series are zero. In 2004 G. Gevorkyan raised the issue that if Cantor's result extends to the Franklin system. The conjecture remains open until now. In the present paper we show however that Kozlov's version remains true for Franklin's system.
KW  - Franklin system
KW  - orthonormal spline system
KW  - trigonometric system
KW  - uniqueness of series
SN  - 1232-9274
ER  -