INTRODUCTION TO COMPLEX ANALYSIS IN SEVERAL VARIABLES

By O. JOMAU

CONTENTS ELEMENTARY THEORY OF SEVERAL COMPLEX VARIABLES GEOMETRY OF CN HOLOMORPHIC FUNCTIONS IN SEVERAL COMPLEX VARIABLES DE?NITION OF A HOLOMORPHIC FUNCTION BASIC PROPERTIES OF HOLOMORPHIC FUNCTIONS PARTIALLY HOLOMORPHIC FUNCTIONS AND THE CAUCHY–RIEMANN DI?ERENTIAL EQUATIONS THE CAUCHY INTEGRAL FORMULA O (U) AS A TOPOLOGICAL SPACE LOCALLY CONVEX SPACES THE COMPACT-OPEN TOPOLOGY ON C (U, E) THE THEOREMS OF ARZEL`A–ASCOLI AND MONTEL POWER SERIES AND TAYLOR SERIES SUMMABLE FAMILIES IN BANACH SPACES POWER SERIES REINHARDT DOMAINS AND LAURENT EXPANSION CONTINUATION ON CIRCULAR AND POLYCIRCULAR DOMAINS HOLOMORPHIC CONTINUATION REPRESENTATION-THEORETIC INTERPRETATION OF THE LAURENT SERIES HARTOGS’ KUGELSATZ, SPECIAL CASE BIHOLOMORPHIC MAPS THE INVERSE FUNCTION THEOREM AND IMPLICIT FUNCTIONS THE RIEMANN MAPPING PROBLEM CARTAN’S UNIQUENESS THEOREM ANALYTIC SETS ELEMENTARY PROPERTIES OF ANALYTIC SETS THE RIEMANN REMOVABLE SINGULARITY THEOREMS HARTOGS’ KUGELSATZ HOLOMORPHIC DI?ERENTIAL FORMS MULTILINEAR FORMS COMPLEX DI?ERENTIAL FORMS THE INHOMOGENOUS CAUCHY–RIEMANN DI?ERENTIAL EQUATIONS DOLBEAUT’S LEMMA THE KUGELSATZ OF HARTOGS CONTINUATION ON TUBULAR DOMAINS CONVEX HULLS HOLOMORPHICALLY CONVEX HULLS BOCHNER’S THEOREM CARTAN–THULLEN THEORY HOLOMORPHICALLY CONVEX SETS DOMAINS OF HOLOMORPHY THE THEOREM OF CARTAN–THULLEN HOLOMORPHICALLY CONVEX REINHARDT DOMAINS LOCAL PROPERTIES OF HOLOMORPHIC FUNCTIONS LOCAL REPRESENTATION OF A HOLOMORPHIC FUNCTION GERM OF A HOLOMORPHIC FUNCTION THE ALGEBRAS OF FORMAL AND OF CONVERGENT POWER SERIES THE WEIERSTRASS THEOREMS THE WEIERSTRASS DIVISION FORMULA THE WEIERSTRASS PREPARATION THEOREM ALGEBRAIC PROPERTIES OF C {Z1, , ZN} HILBERT’S NULLSTELLENSATZ GERMS OF A SET THE RADICAL OF AN IDEAL HILBERT’S NULLSTELLENSATZ FOR PRINCIPAL IDEALS REGISTER OF SYMBOLS