Generalized Bloch Mappings in Complex Hilbert Space
Canadian journal of mathematics, Tome 29 (1977) no. 2, pp. 299-306

Voir la notice de l'article provenant de la source Cambridge University Press

Anderson, Clunie and Pommerenke defined and studied the family of Bloch functions on the unit disc (see [1]). This family strictly contains the space of bounded analytic functions. However, all Bloch functions are normal and therefore enjoy the “nice” properties of normal functions. The importance of the Bloch function concept is the combination of their richness as a family and their “nice” behavior.
Wicker, Fletcher D. Generalized Bloch Mappings in Complex Hilbert Space. Canadian journal of mathematics, Tome 29 (1977) no. 2, pp. 299-306. doi: 10.4153/CJM-1977-033-9
@article{10_4153_CJM_1977_033_9,
     author = {Wicker, Fletcher D.},
     title = {Generalized {Bloch} {Mappings} in {Complex} {Hilbert} {Space}},
     journal = {Canadian journal of mathematics},
     pages = {299--306},
     year = {1977},
     volume = {29},
     number = {2},
     doi = {10.4153/CJM-1977-033-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-033-9/}
}
TY  - JOUR
AU  - Wicker, Fletcher D.
TI  - Generalized Bloch Mappings in Complex Hilbert Space
JO  - Canadian journal of mathematics
PY  - 1977
SP  - 299
EP  - 306
VL  - 29
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-033-9/
DO  - 10.4153/CJM-1977-033-9
ID  - 10_4153_CJM_1977_033_9
ER  - 
%0 Journal Article
%A Wicker, Fletcher D.
%T Generalized Bloch Mappings in Complex Hilbert Space
%J Canadian journal of mathematics
%D 1977
%P 299-306
%V 29
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-033-9/
%R 10.4153/CJM-1977-033-9
%F 10_4153_CJM_1977_033_9

[1] 1. Anderson, J. M., Clunie, J., and Pommerenke, Ch., On Bloch functions and normal functions, J. Reine Angew. Math. 270 (1974), 12–37. Google Scholar

[2] 2. Earle, Clifford J. and Hamilton, Richard S., A fixed point theorem for holomorphic mappings, Global Analysis, Proc. of Symposium in Pure Math. XVI, (Amer. Math. Soc. Providence, R.I., 196.5). Google Scholar

[3] 3. Hahn, Kyong T.. Hyperbolic geometry on the unit ball of a complex Hilbert space, to appear. Google Scholar

[4] 4. Holomorphic mappings of the hyperbolic space into the complex Euclidean space and the Bloch theorem, Can. J. Math. 27 (1975), 446–4, 58. Google Scholar

[5] 5. Hille, Einar, and Phillips, Ralph S., Functional analysis and semigroups, Amer. Math. Soc. Colloquium Publications, Vol. 81 (Amer. Math. Soc, Providence, R.I. 1957). Google Scholar

[6] 6. Nachbin, Leopoldo, Topology on spaces of holomorphic mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band Iff (Springer Verlag, New York, 1969). Google Scholar

Cité par Sources :