Parametric representations of semi-complete vector fields on the unit balls in Cn and in Hilbert space
Aharonov, Dov ; Elin, Mark ; Reich, Simeon ; Shoikhet, David
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 10 (1999), p. 229-253 / Harvested from Biblioteca Digitale Italiana di Matematica

We present several characterizations and representations of semi-complete vector fields on the open unit balls in complex Euclidean and Hilbert spaces.

Vengono presentate alcune caratterizzazioni e rappresentazioni di campi vettoriali semi-completi sulle palle unitarie aperte degli spazi complessi euclidei e di Hilbert.

Publié le : 1999-12-01
@article{RLIN_1999_9_10_4_229_0,
     author = {Dov Aharonov and Mark Elin and Simeon Reich and David Shoikhet},
     title = {Parametric representations of semi-complete vector fields on the unit balls in \( \mathbb{C}^{n} \) and in Hilbert space},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {10},
     year = {1999},
     pages = {229-253},
     zbl = {1036.32017},
     mrnumber = {1767931},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1999_9_10_4_229_0}
}
Aharonov, Dov; Elin, Mark; Reich, Simeon; Shoikhet, David. Parametric representations of semi-complete vector fields on the unit balls in \( \mathbb{C}^{n} \) and in Hilbert space. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 10 (1999) pp. 229-253. http://gdmltest.u-ga.fr/item/RLIN_1999_9_10_4_229_0/

[1] Abate, M., The infinitesimal generators of semigroups of holomorphic maps. Ann. Mat. Pura Appl., 161, 1992, 161-180. | MR 1174816 | Zbl 0758.32013

[2] Berkson, E. - Porta, H., Semigroups of analytic functions and composition operators. Michigan Math. J., 25, 1978, 101-115. | MR 480965 | Zbl 0382.47017

[3] Cowen, C. C. - Maccluer, B. D., Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton, FL 1995. | MR 1397026 | Zbl 0873.47017

[4] Dineen, S., The Schwarz Lemma. Clarendon Press, Oxford1989. | MR 1033739 | Zbl 0708.46046

[5] Franzoni, T. - Vesentini, E., Holomorphic Maps and Invariant Distances. North Holland, Amsterdam 1980. | MR 563329 | Zbl 0447.46040

[6] Goebel, K. - Reich, S., Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings. Dekker, New York-Basel 1984. | MR 744194 | Zbl 0537.46001

[7] Hefer, H., Zur Funktionentheorie mehrerer Veränderlichen. Über eine Zerlegung analytischer Funktionen und die Weilsche Integraldarstellung. Math. Ann., 122, 1950, 276-278. | MR 39082 | Zbl 0038.23801

[8] Henkin, G. - Leiterer, J., Theory of Functions on Complex Manifolds. Birkhäuser, Basel 1984. | MR 774049 | Zbl 0573.32001

[9] Hayden, T. L. - Suffridge, T. J., Biholomorphic maps in Hilbert space have a fixed point. Pacific J. Math., 38, 1971, 419-422. | MR 305158 | Zbl 0229.47043

[10] Isidro, J. M. - Stacho, L. L., Holomorphic Automorphism Groups in Banach Spaces: An Elementary Introduction. North-Holland, Amsterdam 1984. | MR 779821 | Zbl 0561.46022

[11] Khatskevich, V. - Reich, S. - Shoikhet, D., Complex dynamical systems on bounded symmetric domains. Electronic J. Differential Equations, 19, 1997, 1-9. | MR 1476066 | Zbl 0890.34051

[12] Martin Jr, R. H., Differential equations on closed subsets of a Banach space. Trans. Amer. Math. Soc., 179, 1973, 399-414. | MR 318991 | Zbl 0293.34092

[13] Martin Jr, R. H., Nonlinear Operators and Differential Equations in Banach Spaces. Wiley, New York1976. | MR 492671 | Zbl 0333.47023

[14] Reich, S., Minimal displacement of points under weakly inward pseudo-Lipschitzian mappings. Rend. Mat. Acc. Lincei, s. 8, v. 59, 1975, 40-44. | MR 451058 | Zbl 0347.47039

[15] Reich, S., On fixed point theorems obtained from existence theorems for differential equations. J. Math. Anal. Appl., 54, 1976, 26-36. | MR 402554 | Zbl 0328.47034

[16] Reich, S., Averaged mappings in the Hilbert ball. J. Math. Anal. Appl., 109, 1985, 199-206. | MR 796053 | Zbl 0588.47061

[17] Reich, S. - Shoikhet, D., Generation theory for semigroups of holomorphic mappings. Abstract and Applied Analysis, 1, 1996, 1-44. | MR 1390558 | Zbl 0945.46026

[18] Reich, S. - Shoikhet, D., Semigroups and generators on convex domains with the hyperbolic metric. Rend. Mat. Acc. Lincei, s. 9, v. 8, 1997, 231-250. | MR 1631605 | Zbl 0905.47056

[19] Shabat, B.V., Introduction to Complex Analysis Part II. Functions of Several Variables. Trans. Math. Monographs, 110, American Math. Soc., Providence, RI1992. | MR 1192135 | Zbl 0799.32001

[20] Upmeier, H., Jordan Algebras in Analysis, Operator Theory and Quantum Mechanics. CBMS-NSF Regional Conference Series in Math., American Math. Soc., Providence, RI1987. | MR 874756 | Zbl 0608.17013