Moebius-invariant algebras in balls
Annales de l'Institut Fourier, Tome 33 (1983) no. 2, p. 19-41
On démontre que dans l’algèbre de Fréchet C(B) il y a exactement trois sous-algèbres Y qui sont fermées, qui contiennent des fonctions non constantes, et qui sont invariantes dans le sens suivant : fΨY lorsque fY et Ψ est une application biholomorphe de la boule unité ouverte B de C n sur B. Ce sont (i) l’algèbre des fonctions holomorphes dans B, (ii) l’algèbre des fonctions f dont les conjuguées f ¯ sont holomorphes, (iii) C(B).
It is proved that the Fréchet algebra C(B) has exactly three closed subalgebras Y which contain nonconstant functions and which are invariant, in the sense that fΨY whenever fY and Ψ is a biholomorphic map of the open unit ball B of C n onto B. One of these consists of the holomorphic functions in B, the second consists of those whose complex conjugates are holomorphic, and the third is C(B).
@article{AIF_1983__33_2_19_0,
     author = {Rudin, Walter},
     title = {Moebius-invariant algebras in balls},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {33},
     number = {2},
     year = {1983},
     pages = {19-41},
     doi = {10.5802/aif.914},
     mrnumber = {699485},
     zbl = {0487.32012},
     mrnumber = {84m:32023},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1983__33_2_19_0}
}
Rudin, Walter. Moebius-invariant algebras in balls. Annales de l'Institut Fourier, Tome 33 (1983) no. 2, pp. 19-41. doi : 10.5802/aif.914. http://www.numdam.org/item/AIF_1983__33_2_19_0/

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