Geodesic
Canonical representation of eiconals algebra of three-ray star
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 51, Tome 506 (2021), pp. 57-78 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The paper considers a metric graph of the simplest structure, which is a three-ray star with edges of different lengths in pairs. For it, all steps of the procedure that reduces the eikonal algebra of the graph to the canonical form, are described in detail. Using this form, the spectrum of the algebra is equipped with a graph structure. 
@article{ZNSL_2021_506_a6,
     author = {A. V. Kaplun},
     title = {Canonical representation of eiconals algebra of three-ray star},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {57--78},
     year = {2021},
     volume = {506},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a6/}
}
TY  - JOUR
AU  - A. V. Kaplun
TI  - Canonical representation of eiconals algebra of three-ray star
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2021
SP  - 57
EP  - 78
VL  - 506
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a6/
LA  - ru
ID  - ZNSL_2021_506_a6
ER  - 
%0 Journal Article
%A A. V. Kaplun
%T Canonical representation of eiconals algebra of three-ray star
%J Zapiski Nauchnykh Seminarov POMI
%D 2021
%P 57-78
%V 506
%U http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a6/
%G ru
%F ZNSL_2021_506_a6
A. V. Kaplun. Canonical representation of eiconals algebra of three-ray star. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 51, Tome 506 (2021), pp. 57-78. http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a6/

[1] M. I. Belishev, N. Wada, “On revealing graph cycles via boundary measurements”, Inverse Problems, 25:10 (2009), 105011, 25 pp. | DOI | MR | Zbl

[2] M. I. Belishev, N. Wada, “A C*-algebra associated with dynamics on a graph of strings”, J. Math. Soc. Japan, 67:3 (2015), 1239–1274 | DOI | MR | Zbl

[3] M. I. Belishev, A. V. Kaplun, “Eikonal algebra on a graph of simple structure”, Eurasian J. Math. Comp. Appl., 6:3 (2018), 4–33

[4] M. I. Belishev, A. V. Kaplun, Kanonicheskoe predstavlenie S*-algebry eikonalov metricheskogo grafa, POMI PREPRINT-2, 2021

[5] Zh. Diksme, S*-algebry i ikh predstavleniya, Nauka, M., 1974; J. Dixmier, Les $C^*$-algebrae et leurs represebtations, Gauthier-Villars Ed, Paris, 1969 ; English translation: J. Dixmier, C*-algebras, North-Holland Publ. Co., Amsterdam, 1977 | Zbl | Zbl

[6] G.J.Murphy, $C^*$-Algebras and Operator Theory, Academic Press, San Diego, 1990 | Zbl