Geodesic
On Walsh series with monotone coefficients
Izvestiya. Mathematics , Tome 63 (1999) no. 1, pp. 37-55

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that if $a_n\downarrow 0$ and $\sum_{n=0}^\infty a_n^2=+\infty$ then the Walsh series $\sum_{n=0}^\infty a_nW_n(x)$ has the following property. For any measurable function $f(x)$ which is finite almost everywhere, there are numbers $\delta_n=0,\pm 1$ such that the series $\sum_{n=0}^\infty\delta_na_nW_n(x)$ converges to $f(x)$ almost everywhere. This assertion complements and strengthens previously known results about universal Walsh series and Walsh null-series. 
@article{IM2_1999_63_1_a1,
     author = {G. G. Gevorkyan and K. A. Navasardyan},
     title = {On {Walsh} series with monotone coefficients},
     journal = {Izvestiya. Mathematics },
     pages = {37--55},
     publisher = {mathdoc},
     volume = {63},
     number = {1},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1999_63_1_a1/}
}
TY  - JOUR
AU  - G. G. Gevorkyan
AU  - K. A. Navasardyan
TI  - On Walsh series with monotone coefficients
JO  - Izvestiya. Mathematics 
PY  - 1999
SP  - 37
EP  - 55
VL  - 63
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1999_63_1_a1/
LA  - en
ID  - IM2_1999_63_1_a1
ER  - 
%0 Journal Article
%A G. G. Gevorkyan
%A K. A. Navasardyan
%T On Walsh series with monotone coefficients
%J Izvestiya. Mathematics 
%D 1999
%P 37-55
%V 63
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1999_63_1_a1/
%G en
%F IM2_1999_63_1_a1
G. G. Gevorkyan; K. A. Navasardyan. On Walsh series with monotone coefficients. Izvestiya. Mathematics , Tome 63 (1999) no. 1, pp. 37-55. http://geodesic.mathdoc.fr/item/IM2_1999_63_1_a1/