ABSTRACT

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|115 pages

Normed Spaces and Differential Calculus

chapter 1|10 pages

Normed Spaces

chapter 2|15 pages

Linear Maps

chapter 3|8 pages

Multilinear Maps

chapter 4|16 pages

Polynomials

chapter 5|16 pages

Differentiable Maps

chapter 6|10 pages

Mean Value Theorem

chapter 7|25 pages

Higher Differentials

chapter 8|13 pages

Finite Expansions and Taylor's Formula

part II|117 pages

Holomorphic Mappings

chapter 10|12 pages

The Strong Maximum Modulus Theorem

chapter 11|18 pages

Power Series

chapter 12|7 pages

Analytic Mappings

chapter 13|19 pages

Holomorphic Mappings

chapter 14|23 pages

Gâteaux Holomorphy

chapter 15|18 pages

Radius of Boundedness

part III|138 pages

Topologies on Spaces of Holomorphic Mappings

chapter 16|21 pages

The Compact-Open Topology on H(U;F)

chapter 17|26 pages

The Nachbin Topology on H(U;F)

chapter 18|15 pages

The Bornological Topology on H(U;F)

chapter 19|23 pages

Domains of Holomorphy

chapter 20|21 pages

The Levi Problem in Banach Spaces

chapter 21|30 pages

Spaces of Holomorphic Germs