Dissipative holomorphic functions, Bloch radii, and the Schwarz lemma

Journal d'Analyse Mathematique

Volumn 82, Issue , 2000, Pages 221-232

  Harris, Lawrence A ^a   Reich, Simeon ^b   Shoikhet, David ^c  

^a UNIVERSITY OF KENTUCKY   (United States)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^c International College of Technology   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034355443     PISSN: 00217670     EISSN: 15658538     Source Type: Journal    
DOI: 10.1007/BF02791228     Document Type: Article

References (17)

1. D. Aharonov, S. Reich and D. Shoikhet, Flow invariance conditions for holomorphic mappings in Banach spaces, Math. Proc. Royal Irish Acad. 99A (1999), 93-104.
2. M. G. Crandall and T. M. Liggett, Generation of semigroups of nonlinear transformations on general Banach spaces, Amer. J. Math. 93 (1971), 265-298.
3. N. Dunford and J. T. Schwartz, Linear Operators, Part 1, Wiley, New York, 1957.
4. S. Dineen, The Schwarz Lemma, Clarendon Press, Oxford, 1989.
5. C. J. Earle and R. S. Hamilton, A fixed point theorem for holomorphic mappings, in Global Analysis, Proc. Sympos. Pure Math. XVI, Amer. Math. Soc., Providence, RI, 1970, pp. 61-65.
6. L. A. Harris, A continuous form of Schwarz's lemma in normed linear spaces, Pacific J. Math. 38 (1971), 635-639.
7. L. A. Harris, The numerical range of holomorphic functions in Banach spaces, Amer. J. Math. 93 (1971), 1005-1019.
8. L. A. Harris, On the size of balls covered by analytic transformations, Monatshefte Math. 83 (1977), 9-23.
9. G. Lumer and R. S. Phillips, Dissipative operators in a Banach space, Pacific J. Math. 11 (1961), 679-698.
10. R. H. Martin, Jr., Differential equations on closed subsets of a Banach space, Trans. Amer. Math. Soc. 179 (1973), 399-414.
11. R. H. Martin, Jr., Nonlinear Operators and Differential Equations in Banach Spaces, Wiley, New York, 1976.
12. Z. Nehari, Conformal Mapping, McGraw-Hill, New York, 1952.
13. S. Reich, A nonlinear Hille-Yosida theorem in Banach spaces, J. Math. Anal. Appl. 84 (1981), 1-5.
14. S. Reich and D. Shoikhet, Generation theory for semigroups of holomorphic mappings in Banach spaces, Abstract and Applied Analysis 1 (1996), 1-44.
15. S. Reich and D. Shoikhet, Semigroups and generators on convex domains with the hyperbolic metric, Atti Accad. Naz. Lincei 8 (1997), 231-250.
16. J. T. Schwartz, Nonlinear Functional Analysis, Gordon and Breach, New York, 1969.
17. K. Yosida, Functional Analysis, Springer, Berlin, 1971.