The Carathéodory metric of the annulus
HTML articles powered by AMS MathViewer
- by R. R. Simha PDF
- Proc. Amer. Math. Soc. 50 (1975), 162-166 Request permission
Abstract:
An explicit formula is given for the Carathéodory metric of the annulus in the complex plane. The infinitesimal Carathéodory metric, which is just the norm of the differentiation at a point regarded as a functional on the algebra of holomorphic functions, is also determined.References
- Lars V. Ahlfors, Bounded analytic functions, Duke Math. J. 14 (1947), 1–11. MR 21108
- Lars V. Ahlfors, Open Riemann surfaces and extremal problems on compact subregions, Comment. Math. Helv. 24 (1950), 100–134. MR 36318, DOI 10.1007/BF02567028
- Jacques Chaumat, Dérivations ponctuelles continues dans les algébres de fonctions, C. R. Acad. Sci. Paris Sér. A-B 269 (1969), A347–A350 (French). MR 247475
- R. Courant and D. Hilbert, Methoden der mathematischen Physik. I, Heidelberger Taschenbücher, Band 30, Springer-Verlag, Berlin-New York, 1968 (German). Dritte Auflage. MR 0344038
- Helmut Grunsky, Eindeutige beschränkte Funktionen in mehrfach zusammenhängenden Gebieten. I, Jber. Deutsch. Math.-Verein. 50 (1940), 230–255 (German). MR 3807
- Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker, Inc., New York, 1970. MR 0277770
- B. V. Limaye and R. R. Simha, Deficiencies of certain real uniform algebras, Canadian J. Math. 27 (1975), 121–132. MR 383081, DOI 10.4153/CJM-1975-015-x
- John Wermer, Bounded point derivations on certain Banach algebras, J. Functional Analysis 1 (1967), 28–36. MR 0215105, DOI 10.1016/0022-1236(67)90025-0
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 50 (1975), 162-166
- MSC: Primary 30A40; Secondary 46J10
- DOI: https://doi.org/10.1090/S0002-9939-1975-0379831-8
- MathSciNet review: 0379831