Holomorphy and Calculus in Normed SPates  book cover
1st Edition

Holomorphy and Calculus in Normed SPates

ISBN 9780824772314
Published April 29, 1985 by CRC Press
440 Pages

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Book Description

This book presents a systematic introduction to the theory of holomorphic mappings in normed spaces which has been scattered throughout the literature. It gives the necessary, elementary background for all branches of modern mathematics involving differential calculus in higher dimensional spaces.

Table of Contents

Part I: Normeo Spaces and Differential Calculus 1. Normed Spaces 2. Linear Maps 3. Multilinear Maps 4. Polynomials 5. Differential Maps 6. Mean Value Theorem 7. Higher Differentials 8. Finite Expansions and Taylor's Formula Part II: Holomorphic Mappings 9. Holomorphic Functions of a Complex Variable 10. The Strong Maximum Modulus Theorem 11. Power Series 12. Analytic Mappings 13. Holomorphic Mappings 14. Gateaux Ho1omorphy 15. Radius of Boundedness Part III: Topologies on Spaces of Holomorphic Mappings 16. The Compact Open Topology on H(U;F) 17. The Nachbin Topology on H(U;F) 18. The Bornological Topology on H{U;F) 19. Domains of Holomorphy 20. The Levi Problem in Banach Spaces 21. Spaces of Holomorphic Germs

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