Geodesic
Polynomial as a sum of periodic functions
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 5 (2013) no. 2, pp. 178-179 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is proved that an arbitrary polynomial of degree $n$ representatives as a sum of periodic functions, the minimum number of terms in this sum is $n+1$.
Keywords: periodic functions; counterexamples in the analysis. 
@article{VYURM_2013_5_2_a29,
     author = {A. Yu. Evnin},
     title = {Polynomial as a sum of periodic functions},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {178--179},
     year = {2013},
     volume = {5},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2013_5_2_a29/}
}
TY  - JOUR
AU  - A. Yu. Evnin
TI  - Polynomial as a sum of periodic functions
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
PY  - 2013
SP  - 178
EP  - 179
VL  - 5
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VYURM_2013_5_2_a29/
LA  - ru
ID  - VYURM_2013_5_2_a29
ER  - 
%0 Journal Article
%A A. Yu. Evnin
%T Polynomial as a sum of periodic functions
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
%D 2013
%P 178-179
%V 5
%N 2
%U http://geodesic.mathdoc.fr/item/VYURM_2013_5_2_a29/
%G ru
%F VYURM_2013_5_2_a29
A. Yu. Evnin. Polynomial as a sum of periodic functions. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 5 (2013) no. 2, pp. 178-179. http://geodesic.mathdoc.fr/item/VYURM_2013_5_2_a29/

[1] Evnin A. Yu., “The period of the sum of two periodic functions”, Vestnik YuUrGU. Seriya “Matematika, fizika, khimiya”, 2(42):5 (2005), 56–61 (in Russ.) | Zbl

[2] Evnin A. Yu., “The example of the bijective mapping $f:\mathbb{R}\to\mathbb{R}$ such that $f$ is everywhere discontinuous, but an inverse of the $f$ is continuous at a countable set of points”, Vestnik YuUrGU. Seriya «Matematika. Mekhanika. Fizika», 10(227):4 (2011), 38–39 (in Russ.) | Zbl

[3] Evnin A. Yu., Shved D. A., “Functions' representability as a sum of a finite number of periodic functions”, Matematika v shkole, 2013, no. 5, 72–74 (in Russ.)