Semigroups and generators on convex domains with the hyperbolic metric

Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni

Volumn 8, Issue 4, 1997, Pages 231-250

  Reich, Simeon ^a   Shoikhet, David ^b  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b International College of Technology   (Israel)

Author keywords

Banach space; Generator; Holomorphic mapping; Hyperbolic metric; Monotone operator

Indexed keywords

EID: 0347173753     PISSN: 11206330     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (34)

1. M. ABATE, Horospheres and iterates of holomorphic maps. Math. Z., 198, 1988, 225-238.
2. M. ABATE, The infinitesimal generators of semigroups of holomorphic maps. Ann. Mat. Pura Appl., 161, 1992, 167-180.
3. M. ABATE - J. P. VIGUÉ, Common fixed points in hyperbolic Riemann surfaces and convex domains. Proc. Amer. Math. Soc., 112, 1991, 503-512.
4. L. AIZENBERG - S. REICH - D. SHOIKHET, One-sided estimaes for the existence of null points of holomorphic mappings in Banach spaces. J. Math. Anal. Appl., 203, 1996, 38-54.
5. J. ARAZY, An application of infinite dimensional holomorphy to the geometry of Banach spaces. Lecture Notes in Math., vol. 1267, Springer, Berlin 1987, 122-150.
6. V. BARBU, Nonlinear Semigroups and Differential Equations in Banach Spaces. Noordhoff, Leyden 1976.
7. E. BERKSON - H. PORTA, Semigroups of analytic functions and composition operators. Michigan Math. J., 25, 1978, 101-115.
8. H. BRÉZIS, Opérateurs Maximaux Monotones. North Holland, Amsterdam 1973.
9. H. CARTAN, Sur les rétractions d'une variété. C. R. Acad. Sci. Paris, 303, 1986, 715-716.
10. P. CHERNOFF - J. E. MARSDEN, On continuity and smoothness of group actions. Bull. Amer. Math. Soc., 76, 1970, 1044-1049.
11. M. G. CRANDALL - T. M. LIGGETT, Generation of semigroups of nonlinear transformations on general Banach spaces. Amer. J. Math., 93, 1971, 265-298.
12. S. DINEEN, The Schwarz Lemma. Clarendon Press, Oxford 1989.
13. S. DINEEN - P. M. TIMONEY - J. P. VIGUÉ, Pseudodistances invariantes sur les domaines d'un espace localement convexe. Ann. Scuola Norm. Sup. Pisa, 12, 1985, 515-529.
14. C. J. EARLE - R. S. HAMILTON, A fixed point theorem for holomorphic mappings. Proc. Symp. Pure Math., vol. 16, Amer. Math. Soc., Providence, RI, 1970, 61-65.
15. T. FRANZONI - E. VESENTINI, Holomorphic Maps and Invariant Distances. North Holland, Amsterdam 1980.
16. I. I. GIKHMAN - A. V. SKOROKHOD, Theory of Random Processes. Nauka, Moscow 1973.
17. K. GOEBEL - S. REICH, Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings. Dekker, New York-Basel 1984.
18. L. A. HARRIS, Schwarz-Pick systems of pseudometrics for domains in normed linear spaces. Advances in Holomorphy, North Holland, Amsterdam 1979, 345-406.
19. T. E. HARRIS, The Theory of Branching Processes. Springer, Berlin 1963.
20. U. HELMKE - B. MOORE, Optimization and Dynamical Systems. Springer, London 1994.
21. M. E. JACOBSON, Computation of extinction probabilities for the Bellman-Harris branching process. Math. Biosciences, 77, 1985, 173-177.
22. V. KHATSKEVICH - S. REICH - D. SHOIKHET, Ergodic type theorems for nonlinear semigroups with holomorphic generators. Recent Developments in Evolution Equations, Pitman Research Notes in Math., vol. 324, 1995, 191-200.
23. V. KHATSKEVICH - S. REICH - D. SHOIKHET, Global implicit function and fixed point theorems for holomorphic mappings and semigroups. Complex Variables, 28, 1996, 347-356.
24. M. A. KRASNOSELSKI - P. P. ZABREIKO, Geometrical Methods of Nonlinear Analysis. Springer, Berlin 1984.
25. n. Advances Math., 81, 1990, 90-98.
26. P. MAZET - J. P. VIGUÉ, Points fixes d'une application holomorphe d'un domaine borné dans lui-même. Acta Math., 166, 1991, 1-26.
27. W. RUDIN, The fixed point sets of some holomorphic maps. Bull. Malaysian Math. Soc., 1, 1978, 25-28.
28. B. A. SEVASTYANOV, Branching Processes. Nauka, Moscow 1971.
29. I. SHAFRIR, Coaccretive operators and firmly nonexpansive mappings in the Hilbert ball. Nonlinear Analysis, 18, 1992, 637-648.
30. H. UPMEIER, Jordan Algebras in Analysis, Operator Theory and Quantum Mechanics. CBMS-NSF Regional Conference Series in Math., AMS, Providence 1987.
31. E. VESENTINI, Semigroups of holomorphic isometries. Advances Math., 65, 1987, 272-306.
32. E. VESENTINI, Krein spaces and holomorphic isometries of Cartan domains. In: S. COEN (ed.), Geometry and Complex Variables. Dekker, New York 1991, 409-413.
33. E. VESENTINI, Semigroups of holomorphic isometries. In: S. COEN (ed.), Complex Potential Theory. Kluwer, Dordrecht 1994, 475-548.
34. K. YOSIDA, Functional Analysis. Springer, Berlin 1968.