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OverviewThe present report on spaces of holomorphic mappings was prepared for the Sexto Coloquio Brasileiro de Matematica (Po~os de Caldas, Minas Gerais, Brazil, July 1967). I also had the oppor- tunity of giving a series of lectures on this material while I was a visiting member at the Center for Theoretical Studies of the University of Miami (Coral Gables, Florida, USA, February 1968). The preparation of this report was sponsored in part by the USA National Science Foundation through a grant to the University of Rochester. I am glad to thank Professors Paul R. Halmos and Peter J. Hilton for accepting my text as part of the series Ergebnisse der Mathematik und ihre Grenzgebiete. Rochester, New York 1968 Leopoldo Nachbin Contents 1. Introduction. 1 2. Notation and Terminology 4 3. Continuous Polynomials 6 4. Convergent Power Series 11 5. Holomorphic Mappings. 16 6. The Cauchy Integral 20 7. Convergence of Taylor Series. 26 8. Topology on the Space of all Holomorphic Mappings 31 9. Holomorphy Types. 34 10. Differentiation of Holomorphy Types . 38 II. Topology on Spaces of Holomorphic Mappings. 43 12. Bounded Subsets. 49 13. Relatively Compact Subsets . 54 14. The Current Holomorphy Type 59 15. Bibliographical References. 62 Subject Index 65 1. Full Product DetailsAuthor: Leopoldo NachbinPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Volume: 47 Weight: 0.250kg ISBN: 9783540044703ISBN 10: 3540044701 Pages: 76 Publication Date: 01 January 1969 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Out of Print Availability: Out of stock  Table of Contents1. Introduction.- 2. Notation and Terminology.- 3. Continuous Polynomials.- 4. Convergent Power Series.- 5. Holomorphic Mappings.- 6. The Cauchy Integral.- 7. Convergence of Taylor Series.- 8. Topology on the Space of all Holomorphic Mappings.- 9. Holomorphy Types.- 10. Differentiation of Holomorphy Types.- 11. Topology on Spaces of Holomorphic Mappings.- 12. Bounded Subsets.- 13. Relatively Compact Subsets.- 14. The Current Holomorphy Type.- 15. Bibliographical References.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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