Geodesic
Some boundary properties of abstract analytic functions, and their applications
Sbornik. Mathematics, Tome 29 (1976) no. 4, pp. 453-474 
A. A. Danilevich. Some boundary properties of abstract analytic functions, and their applications. Sbornik. Mathematics, Tome 29 (1976) no. 4, pp. 453-474. http://geodesic.mathdoc.fr/item/SM_1976_29_4_a2/
@article{SM_1976_29_4_a2,
     author = {A. A. Danilevich},
     title = {Some boundary properties of abstract analytic functions, and their applications},
     journal = {Sbornik. Mathematics},
     pages = {453--474},
     year = {1976},
     volume = {29},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_29_4_a2/}
}
TY  - JOUR
AU  - A. A. Danilevich
TI  - Some boundary properties of abstract analytic functions, and their applications
JO  - Sbornik. Mathematics
PY  - 1976
SP  - 453
EP  - 474
VL  - 29
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1976_29_4_a2/
LA  - en
ID  - SM_1976_29_4_a2
ER  - 
%0 Journal Article
%A A. A. Danilevich
%T Some boundary properties of abstract analytic functions, and their applications
%J Sbornik. Mathematics
%D 1976
%P 453-474
%V 29
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1976_29_4_a2/
%G en
%F SM_1976_29_4_a2

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

We study boundary properties of analytic functions of the Hardy and Nevanlinna classes, defined in the unit disk, with values in a Fréchet space $E'$, the strong dual of a locally convex topological space $E$. In particular, necessary and sufficient conditions are given for angular limiting values of these functions to exist almost everywhere on a subset $M$, $\operatorname{mes}M>0$, of the unit circle in the topology of the space $E'$. The results obtained are used to investigate boundary properties of compact families of complex-valued holomorphic functions. Bibliography: 16 titles.

[1] R. Ryan, “Boundary values of analytic vector valued functions”, Proc. Koninkl. Nederl. Akad., Ser. A, 65:5 (1962), 558–572 | MR | Zbl

[2] C. Grossetete, “Sur certaines classes de fonctions harmoniques dans le disque a valeur dans un espace vectoriel topologique localement convexe”, C. r. Acad. scient, 273:22 (1971), A1048–A1051 | MR

[3] C. Grossetete, “Classes de Hardy et de Nevanlinna pour les fonctions holomorphes a valeurs vectorielles”, C. r. Acad. scient, 274:3 (1972), A251–A253 | MR

[4] A. Zygmund, “On the boundary values of functions of several complex variables”, Fundam. math., 36 (1949), 207–235 | MR | Zbl

[5] G. Ts. Tumarkin, “O ravnomernoi skhodimosti nekotorykh posledovatelnostei funktsii”, DAN SSSR, 105:6 (1955), 1151–1154 | MR | Zbl

[6] G. Ts. Tumarkin, “Usloviya skhodimosti granichnykh znachenii analiticheskikh funktsii i priblizheniya na spryamlyaemykh krivykh”, Sovremennye problemy teorii analiticheskikh funktsii, izd-vo «Nauka», Moskva, 1966 | MR

[7] A. A. Danilevich, “Nekotorye primeneniya abstraktnykh analiticheskikh funktsii dlya issledovaniya granichnykh svoistv ryadov golomorfnykh funktsii”, DAN SSSR, 223:1 (1975), 31–34 | MR | Zbl

[8] J. E. Littlewood, “On functions subharmonic in a circle, II”, Proc. London Math. Soc., 28 (1927), 383–394 | DOI

[9] M. A. Evgrafov, Analiticheskie funktsii, izd-vo «Nauka», Moskva, 1970 | MR

[10] E. Bishop, “Analytic functions with values in a Frechet space”, Pacific J. Math., 12:4 (1962), 1177–1192 | MR

[11] I. I. Privalov, Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, Moskva, 1950

[12] I. I. Privalov, Subgarmonicheskie funktsii, Gostekhizdat, Moskva, 1937

[13] M. M. Dei, Normirovannye lineinye prostranstva, IL, Moskva, 1961

[14] U. Rudin, Teoriya funktsii v polikruge, izd-vo «Mir», Moskva, 1974 | MR

[15] C. L. Davis, “Iterated limits in $N_*(U^n)$”, Trans. Amer. Math. Soc., 178 (1973), 139–146 | DOI | MR | Zbl

[16] K. Gofman, Banakhovy prostranstva analiticheskikh funktsii, izd-vo «Nauka», Moskva, 1963