Geodesic
About a structure of exponential monomials on some locally compact abelian groups
Problemy analiza, Tome 1 (2012) no. 1, pp. 3-14 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We describe the structure of some class of exponential monomials on some locally compact abelian groups. The main result of the paper is the next theorem. Let $\tilde{G}$ and $G$ be locally compact abelian groups, $\alpha : \tilde{G}\to G$ be a continuous surjective homomorphism and $H$ be a kernel of $\alpha$. If $\alpha$ is a an open maps from $\tilde{G}$ to $G$ then any exponential monomial $\Phi(t)$ on the group $\tilde{G}$, which satisfy the condition $\Phi(t+h)=\Phi(t)\forall h\in H, t\in \tilde{G}$, can be presented in the form $\Phi(t)=f(\alpha(t))$ for some exponential monomial $f(x)$ on the group $G$. 
@article{PA_2012_1_1_a0,
     author = {S. S. Platonov},
     title = {About a structure of exponential monomials on some locally compact abelian groups},
     journal = {Problemy analiza},
     pages = {3--14},
     year = {2012},
     volume = {1},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PA_2012_1_1_a0/}
}
TY  - JOUR
AU  - S. S. Platonov
TI  - About a structure of exponential monomials on some locally compact abelian groups
JO  - Problemy analiza
PY  - 2012
SP  - 3
EP  - 14
VL  - 1
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/PA_2012_1_1_a0/
LA  - ru
ID  - PA_2012_1_1_a0
ER  - 
%0 Journal Article
%A S. S. Platonov
%T About a structure of exponential monomials on some locally compact abelian groups
%J Problemy analiza
%D 2012
%P 3-14
%V 1
%N 1
%U http://geodesic.mathdoc.fr/item/PA_2012_1_1_a0/
%G ru
%F PA_2012_1_1_a0
S. S. Platonov. About a structure of exponential monomials on some locally compact abelian groups. Problemy analiza, Tome 1 (2012) no. 1, pp. 3-14. http://geodesic.mathdoc.fr/item/PA_2012_1_1_a0/

[1] Schvartz L., “Théorie générate des functions moynne-periodiques”, Ann. of Math., 48:2 (1947), 875–929

[2] Gilbert J. E., “On the ideal structure of some algebras of analytic functions”, Pacif. J. of Math., 35:3 (1978), 625–639 | DOI | MR

[3] Platonov S. S., “Spektralnyi sintez v nekotorykh funktsionalnykh topologicheskikh vektornykh prostranstvakh”, Algebra i analiz, 22:5 (2010), 154–185 | MR

[4] Gurevich D. I., “Kontrprimery k probleme L. Shvartsa”, Funkts. analiz i ego prilozh., 9:2 (1975), 29–35 | MR | Zbl

[5] Schvartz L., “Analyse et synthese harmonique dans les espaces de distributions”, Can. J. Math., 3 (1951), 503–512 | DOI | MR

[6] Szekelyhidi L., Discrete spectral synthesis and its applications, Springer, Berlin, 2006 | MR | Zbl

[7] Lefranc M., “Analyse spectrale sur $Z_n$”, C. R. Acad. Sci. Paris, 246 (1958), 1951–1953 | MR | Zbl

[8] Szekelyhidi L., “On discrete spectral synthesis”, Functional Equation — Results and Advances, eds. Z. Daroczy and Zs. Pales, Kluwer Academic Publishers, Dordrecht, 2002, 263–274 | DOI | MR | Zbl

[9] Bereczky A., Szekelyhidi L., “Spectral synthesis on torsion groups”, J. Math. Anal. Appl., 304 (2005), 607–613 | DOI | MR | Zbl

[10] Platonov S. S., “Spektralnyi sintez v prostranstve funktsii eksponentsialnogo rosta na konechno porozhdennoi abelevoi gruppe”, Algebra i analiz, 24:4 (2012), 182–200 | MR

[11] Szaekelyhidi L., “Spectral synthesis problems on locally compact groups”, Monatsh. Math., 161:2 (2010), 223–232 | DOI | MR

[12] Pontryagin L. S., Nepreryvnye gruppy, Nauka, M., 1973 | MR | Zbl