Several complex variables and banach algebras线性模型和逻辑斯缔回归 第2版

1997-11  

Springer  

Herbert Alexander,John Wermer  

253  

Many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras. While function theory has often been employed to answer algebraic questions such as the existence of idempotents in a Banach algebra, concepts arising from the study of Banach algebras including the maximal ideal space, the Silov boundary, Geason parts, etc. have led to new questions and to new methods of proofs in function theory. This book is concerned with developing some of the principal applications of function theory in several complex variables to Banach algebras. The authors do not presuppose any knowledge of several complex variables on the part of the reader and all relevant material is developed within the text. Furthermore, the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. The third edition of this book contains new material on; maximum modulus algebras and subharmonicity, the hull of a smooth curve, integral kernels, perturbations of the Stone-Weierstrass Theorem, boundaries of analytic varieties, polynomial hulls of sets over the circle, areas, and the topology of hulls. The authors have also included a new chapter containing commentaries on history and recent developments and an updated and expanded reading list.

Preface to the Second Edition Preface to the Third Edition Chapter 1 Preliminaries and Notation Chapter 2 Classical Approximation Theorems Chapter 3 Operational Calculus in One Variable Chapter 4 Differential Forms Chapter 5 The XXX-Operator Chapter 6 The Equation XXXu = f Chapter 7 The Oka-Weil Theorem Chapter 8 Operational Calculus in Several Variables Chapter 9 The Silov Boundary Chapter 10 Maximality and Rado's Theorem Chapter 11 Maximum Modulus Algebras Chapter 12 Hulls of Curves and Arcs Chapter 13 Integral Kernels Chapter 14 Perturbations of the Stone-Weierstrass Theorem Chapter 15 The First Cohomology Group of a Maximal Ideal Space Chapter 16 The XXX-Operator in Smoothly Bounded Domains Chapter 17 Manifolds Without Complex Tangents Chapter 18 Submanifolds of High Dimension Chapter 19 Boundaries of Analytic Varieties Chapter 20 Polynomial Hulls of Sets Over the Circle Chapter 21 Areas Chapter 22 Topology of Hulls Chapter 23 Pseudoconvex sets in C(n) Chapter 24 Examples Chapter 25 Historical Comments and Recent Developments Chapter 26 Appendix Chapter 27 Solutions to Some Exercises Bibliography Index

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