General versions of Glicksberg's theorem concerning zeros of holomorphic maps and of Hurwitz's theorem on sequences of analytic functions is extended to infinite dimensional Banach spaces.
I teoremi di Glicksberg e di Hurwitz sugli zeri di funzioni e sulle successioni di funzioni olomorfe sono generalizzati ad applicazioni olomorfe di spazi di Banach complessi di dimensione infinita.
@article{RLIN_1993_9_4_2_99_0,
author = {Kazimier Wzodarczyk},
title = {The theorems of Glicksberg and Hurwitz for holomorphic maps in complex Banach spaces},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
volume = {4},
year = {1993},
pages = {99-102},
zbl = {0794.46039},
mrnumber = {1233396},
language = {en},
url = {http://dml.mathdoc.fr/item/RLIN_1993_9_4_2_99_0}
}
Wzodarczyk, Kazimier. The theorems of Glicksberg and Hurwitz for holomorphic maps in complex Banach spaces. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 4 (1993) pp. 99-102. http://gdmltest.u-ga.fr/item/RLIN_1993_9_4_2_99_0/
[1] , Functions of One Complex Variable. Graduate Texts in Math., 11, 2nd ed., Springer-Verlag, New York-Berlin-Heidelberg-Tokyo1978. | MR 503901 | Zbl 0277.30001
[2] - , Holomorphic Maps and Invariant Distances. North Holland Mathematics Studies, 40, Amsterdam-New York-Oxford 1980. | MR 563329 | Zbl 0447.46040
[3] , A remark on Rouché's theorem. Amer. Math. Monthly, 83, 1976, 186-187. | MR 396919 | Zbl 0318.30002
[4] , Über die Nullstellen der Bessel'schen Funktion. Math. Ann., 33, 1889, 246-266. | JFM 20.0502.02
[5] , Eine Verallgemeinerung des Rouchéschen Satzes. J. Reine Angew. Math., 160, 1929, 143-150. | JFM 55.0175.05
[6] , Degree Theory. Cambridge Tracts in Math., 73, Cambridge University Press, 1978. | MR 493564 | Zbl 0367.47001
[7] , The Geometry of the Zeros. Math. Surveys, 3, Amer. Math. Soc., New York1949. | MR 31114 | Zbl 0038.15303
[8] , Topology on Spaces of Holomorphic Mappings. Ergebnisse der Math, und ihrer Grenzgebiete, 47, Springer-Verlag, Berlin-Heidelberg-New York1969. | MR 254579 | Zbl 0172.39902
[9] , Mémoire sur la série de Lagrange. J. Ecole Polytech., 22, 1862, 217-218. | JFM 01.0039.03
[10] , Compact analytic mappings of B-spaces and a theorem of Jane Cronin. Comm. Pure Appi. Math., 16, 1963, 253-260. | MR 163178 | Zbl 0124.32703
[11] , Fixed points and invariant domains of expansive holomorphic maps in complex Banach spaces. Adv. Math., to appear. | MR 1317617 | Zbl 0868.47036
[12] , The Rouché theorem for holomorphic maps in complex Banach spaces. Complex Variables Theory Appl., 20, 1992, 71-73. | MR 1284353 | Zbl 0789.46042