Preorder on the set of analytic functions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 5, pp. 681-689.

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

In the paper, we study a preorder, which can be naturally defined on the set of all analytic functions of two complex variables with the help of superpositions of analytic functions of one variable.
Keywords: analytical complexity, superpositions of analytic functions.
@article{JSFU_2023_16_5_a13,
     author = {Maria A. Stepanova},
     title = {Preorder on the set of analytic functions},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {681--689},
     publisher = {mathdoc},
     volume = {16},
     number = {5},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2023_16_5_a13/}
}
TY  - JOUR
AU  - Maria A. Stepanova
TI  - Preorder on the set of analytic functions
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2023
SP  - 681
EP  - 689
VL  - 16
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2023_16_5_a13/
LA  - en
ID  - JSFU_2023_16_5_a13
ER  - 
%0 Journal Article
%A Maria A. Stepanova
%T Preorder on the set of analytic functions
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2023
%P 681-689
%V 16
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2023_16_5_a13/
%G en
%F JSFU_2023_16_5_a13
Maria A. Stepanova. Preorder on the set of analytic functions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 5, pp. 681-689. http://geodesic.mathdoc.fr/item/JSFU_2023_16_5_a13/

[1] A.G.Vitushkin, “A proof of the existence of analytic functions of several variables not representable by linear superpositions of continuously differentiable functions of fewer variables”, Dokl. Akad. Nauk SSSR, 156:6 (1964), 1258–1261 (in Russian) | MR | Zbl

[2] G.M.Henkin, “Nonisomorphism of certain spaces of functions of different numbers of variables”, Funct. Anal. Appl., 1:4 (1967), 306–315 | DOI | MR

[3] A.G.Vitushkin, G.M.Henkin, “Linear superpositions of functions”, Russian Math. Surveys, 22:1 (1967), 77–125 | DOI | MR

[4] A.G.Khovanskii, “The representability of algebroidal functions by superpositions of analytic functions and algebroidal functions of one variable”, Funct. Anal. Appl., 4:2 (1970), 152–156 | DOI | MR | Zbl

[5] V.K.Beloshapka, “Analytic Complexity of Functions of Two Variables”, Russian Journal of Mathematical Physics, 14:3 (2007), 243–249 | DOI | MR | Zbl

[6] V.K.Beloshapka, “Decomposition of Functions of Finite Analytical Complexity”, Journal of Siberian Federal University. Mathematics $\$ Physics, 11:6 (2018), 680–685 | DOI | MR

[7] V.K.Beloshapka, “Stabilizer of a function in the gauge group”, Russ. J. Math. Phys., 24 (2017), 148–152 | DOI | MR | Zbl

[8] M.A.Stepanova, “Analytic complexity of differential algebraic functions”, Sb. Math., 210:12 (2019), 1774–1787 | DOI | MR | Zbl