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Infinite dimensional holomorphy is the study of holomorphic or analytic funcÂ tions over complex topological vector spaces. The terms in this description are easily stated and explained and allow the subject to project itself iniÂ tially, and innocently, as a compact theory with well defined boundaries. However, a comprehensive study would include delving into, and interacting with, not only the obvious topics of topology, several complex variables theory and functional analysis but also, differential geometry, Jordan algebras, Lie groups, operator theory, logic, differential equations and fixed point theory. This diversity leads to a dynamic synthesis of ideas and to an appreciation of a remarkable feature of mathematics - its unity. Unity requires synthesis while synthesis leads to unity. It is necessary to stand back every so often, to take an overall look at one's subject and ask "How has it developed over the last ten, twenty, fifty years? Where is it going? What am I doing?" I was asking these questions during the spring of 1993 as I prepared a short course to be given at Universidade Federal do Rio de Janeiro during the following July. The abundance of suitÂ able material made the selection of topics difficult. For some time I hesitated between two very different aspects of infinite dimensional holomorphy, the geometric-algebraic theory associated with bounded symmetric domains and Jordan triple systems and the topological theory which forms the subject of the present book.

- Series:
**Springer Monographs in Mathematics** - Author:
**SeÃ¡n Dineen PhD, DSc (auth.)** - Year:
**1999** - Publisher:
**Springer-Verlag London** - Language:
**English** - ISBN:
**978-1-4471-1223-5,978-1-4471-0869-6**

- File size:
**21 669 257** - Format:
**pdf**

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This book is based on lectures given at Yale and Kyoto Universities and provides a self-contained detailed exposition of the following subjects: 1) The construction of infinite dimensional measures, 2) Invariance and quasi-invariance of measures under tra...

A systematic, self-contained treatment of the theory of stochastic differential equations in infinite dimensional spaces. Included is a discussion of Schwartz spaces of distributions in relation to probability theory and infinite dimensional stochastic an...

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, and dynamics in infinite-dimensional spaces. In addit...

This work can be recommended as an extensive course in superanalysis, the theory of functions of commuting and anticommuting variables. It follows the so-called functional superanalysis which was developed by J. Schwinger, B. De Witt, A. Rogers, V.S. V...

In a very broad sense, "spaces" are objects of study in geometry, and "functions" are objects of study in analysis. There are, however, deep relations between functions defined on a space and the shape of the space, and the study of these relations is the...

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 fibra...

This book investigates the high degree of symmetry that lies hidden in integrable systems. To that end, differential equations arising from classical mechanics, such as the KdV equation and the KP equations, are used here by the authors to introduce the n...

Problems arising from the study of holomorphic continuation and holomorphic approximation have been central in the development of complex analysis in finitely many variables, and constitute one of the most promising lines of research in infinite dimension...

This volume comprises invited presentations from the 8th International Evoked Potentials Symposium. It is no longer possible to categorise chapters by modality, so the Editors have grouped them under broader headings reflecting the use of Evoked Potential...

Pamela Slim, a former corporate training manager, left her office job twelve years ago to go solo and has enjoyed every bit of it. In her groundbreaking book, based on her popular blog Escape from Cubicle Nation, Slim explores both the emotional issues ...

Production and quality can be significantly impacted if improper selection or inadequate maintenance of temperature and humidity measures. Based on the authors 38 years in the textile industry, this book explains the principles adopted in different humidi...

Graduates face a world of complexity which demands flexibility, adaptability, self-reliance and innovation, but while the development of creativity is embedded in theÂ English National Curriculum and in workplace training, the higher education sector has y...

Today, even as America asserts itself globally, it lacks a grand strategy to replace "containment of communism." In this short, sharp book, Gary Hart outlines a new grand strategy, one directing America's powers to the achievement of its large purposes. ...

Perhaps my love of this text is because I was one of those students who only wanted to know how to use a derivative or integral to solve a physical problem when I took my first calculus class in 1973. Years later when I was visiting MIT looking for econom...

Ramachandra Guha, author of the internationally acclaimed India After Gandhi, profiles nineteen Indians whose ideas had a defining impact on the formation and evolution of our Republic, and presents rare and compelling excerpts from their writings and spe...