440 Pages
by
CRC Press
440 Pages
by
CRC Press
Also available as eBook on:
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.
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
Biography
Soo Bong Chae is Professor of Mathematics at New College of the University of South Florida in Sarasota, Florida.
