Moebius-invariant algebras in balls
Annales de l'Institut Fourier, Volume 33 (1983) no. 2, p. 19-41

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).

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).

@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, Volume 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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