Foundations of Complex Analysis in Non Locally Convex Spaces, Volume 193

1st Edition

Function Theory without Convexity Condition

Print ISBN: 9780444500564
eBook ISBN: 9780080531922
Imprint: JAI Press
Published Date: 11th November 2003
Page Count: 304
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All the existing books in Infinite Dimensional Complex Analysis focus on the problems of locally convex spaces. However, the theory without convexity condition is covered for the first time in this book. This shows that we are really working with a new, important and interesting field.

Theory of functions and nonlinear analysis problems are widespread in the mathematical modeling of real world systems in a very broad range of applications. During the past three decades many new results from the author have helped to solve multiextreme problems arising from important situations, non-convex and non linear cases, in function theory.

Foundations of Complex Analysis in Non Locally Convex Spaces is a comprehensive book that covers the fundamental theorems in Complex and Functional Analysis and presents much new material.

The book includes generalized new forms of: Hahn-Banach Theorem, Multilinear maps, theory of polynomials, Fixed Point Theorems, p-extreme points and applications in Operations Research, Krein-Milman Theorem, Quasi-differential Calculus, Lagrange Mean-Value Theorems, Taylor series, Quasi-holomorphic and Quasi-analytic maps, Quasi-Analytic continuations, Fundamental Theorem of Calculus, Bolzano's Theorem, Mean-Value Theorem for Definite Integral, Bounding and weakly-bounding (limited) sets, Holomorphic Completions, and Levi problem.

Each chapter contains illustrative examples to help the student and researcher to enhance his knowledge of theory of functions.

The new concept of Quasi-differentiability introduced by the author represents the backbone of the theory of Holomorphy for non-locally convex spaces. In fact it is different but much stronger than the Frechet one.

The book is intended not only for Post-Graduate (M.Sc.& Ph.D.) students and researchers in Complex and Functional Analysis, but for a


M.Sc. and Ph.D. students and reseachers in Analysis, especially in Complex and Functional Analysis.

Table of Contents

  1. Fundamental Theorems in F-Spaces.
  2. Theory of Polynomials in F-Spaces.
  3. Fixed-Point and P-Extreme Point.
  4. Bayoumi (Quasi) Differential Calculus.
  5. Generalized Mean-Value Theorem.
  6. Higher Quasi-Differential in F-Spaces.
  7. Quasi-Holomorphic Maps.
  8. New Versions of Main Theorems.
  9. Bounding and Weakly-Bounding Sets.
  10. Levi Problem in Toplogical Spaces.


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© JAI Press 2003
JAI Press
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"...this book is definitely a contribution to the subject..." Richard M. Aron, in: (Mathematical Reviews, 2004)