Infinite Dimensional Holomorphy and Applications

This book presents a set of basic properties of holomorphic mappings between complex normed spaces and between complex locally convex spaces. These properties have already achieved an almost definitive form and should be known to all those interested in the study of infinite dimensional Holomorphy and its applications.The author also makes ``incursions'' into the study of the topological properties of the spaces of holomorphic mappings between spaces of infinite dimension. An attempt is then made to show some of the several topologies that can naturally be considered in these spaces.Infinite dimensional Holomorphy appears as a theory rich in fascinating problems and rich in applications to other branches of Mathematics and Mathematical Physics.

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.

This volume presents the proceedings of the Seventh International Colloquium on Finite or Infinite Dimensional Complex Analysis held in Fukuoka, Japan. The contributions offer multiple perspectives and numerous research examples on complex variables, Clifford algebra variables, hyperfunctions and numerical analysis.

This volume contains contributions on recent results in infinite dimensional harmonic analysis and its applications to probability theory. Some papers deal with purely analytic topics such as Frobenius reciprocity, diffeomorphism groups, equivariant fibrations and Harish-Chandra modules. Several other papers touch upon stochastic processes, in particular Lévy processes. The majority of the contributions emphasize on the algebraic-topological aspects of the theory by choosing configuration spaces, locally compact groups and hypergroups as their basic structures. The volume provides a useful survey of innovative work pertaining to a highly actual section of modern analysis in its pure and applied shapings.

Differential Calculus and Holomorphy

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.

The papers in this volume cover a wide variety of topics in the geometric theory of functions of one and several complex variables, including univalent functions, conformal and quasiconformal mappings, minimal surfaces, and dynamics in infinite-dimensional spaces. In addition, there are several articles dealing with various aspects of approximation theory and partial differential equations. Taken together, the articles collected here provide the reader with a panorama of activity in complex analysis, drawn by a number of leading figures in the field.

Functional Analysis, Holomorphy and Approximation Theory