Geodesic
A comparision of the V- and S-Dini tests. A counterexamples on the symmetrical Dini tests by a type Haar and Walsh systems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2019), pp. 73-95

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

We show that a both conditions are important for symmetrical Dini's test by Price's and generalized Haar's systems; an execution of one of them's cannot guarantee a convergence of Fourier series for any majorants. An accordingly examples are constructived.
Keywords: abelian group, Vilenkin's group, characters system, Price's systems, generalized Haar's systems, Dirichlet's kernels, Dini's test. 
@article{IVM_2019_9_a6,
     author = {V. I. Shcherbakov},
     title = {A comparision of the {V-} and {S-Dini} tests. {A} counterexamples on the symmetrical {Dini} tests by a type {Haar} and {Walsh} systems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {73--95},
     publisher = {mathdoc},
     number = {9},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_9_a6/}
}
TY  - JOUR
AU  - V. I. Shcherbakov
TI  - A comparision of the V- and S-Dini tests. A counterexamples on the symmetrical Dini tests by a type Haar and Walsh systems
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2019
SP  - 73
EP  - 95
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2019_9_a6/
LA  - ru
ID  - IVM_2019_9_a6
ER  - 
%0 Journal Article
%A V. I. Shcherbakov
%T A comparision of the V- and S-Dini tests. A counterexamples on the symmetrical Dini tests by a type Haar and Walsh systems
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2019
%P 73-95
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2019_9_a6/
%G ru
%F IVM_2019_9_a6
V. I. Shcherbakov. A comparision of the V- and S-Dini tests. A counterexamples on the symmetrical Dini tests by a type Haar and Walsh systems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2019), pp. 73-95. http://geodesic.mathdoc.fr/item/IVM_2019_9_a6/