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TABLE OF CONTENTS
PREFACE TO THE AMERICAN EDITION
PREFACE
INTRODUCTION
CHAPTER I: INTEGRAL REPRESENTATION OF EXTERIOR DIFFERENTIAL FORMS AND ITS IMMEDIATE CONSEQUENCES
§1. The Martinelli-Bochner-Koppelman formula
§2. Theorems on the saltus of forms
§3. Characterization of the trace of a holomerphic form on the boundary of a domain
§4. Some cases of solvability of the a-problem
CHAPTER II: FORMS ORTHOGONAL TO HOLOMORPHIC FORMS
§5. Polynomials orthogonal to holomorphic functions
§6. Forms orthogonal to holomorphic forms: the case of strictly pseudoconvex domains
§7. The general case
§8. Converse theorems
CHAPTER III: Properties of $overline{partial}$-closed forms of type $(p,n-1)$
§9. The theorems of Runge and Morera
§10. The f ilst Cousin problem, separation of singularities and domains of existence
§11. Theorems of approximation on compact sets
CHAPTER IV: SOME APPLICATIONS
§12. Generalization of the theorems of Hartogs and F. and M. Riesz
§13. On the general form of integral representations of holomorphic functions
§14. Representation of distributions in D' (R^(2n-1)') by a-closed exterior differential Forms of type (n, n -- 1)
§15. Multiplication of distributions in D' (R^(2n-1))
BRIEF HISTORICAL SURVEY AND OPEN PROBLEMS FOR CHAPTERS I-IV
CHAPTER V: Integral properties characterizing $overline{partial}$-closed differential forms and holomorphic functions
§16. A characteristic property of a-closed forms and forms of class B
§17. Holomorphy of continuous functions representable by the Martinelli-Bochner integral; criteria for the holomorphy of integrals of the Martinelli-Bochner type
§18. The traces of holomorphic functions on the Shilov boundary of a circular domain
§19. Computation of an integral of Martinelli-Bochner type for the case of the ball
§20. Differential boundary conditions for the holomorphy of functions
CHAPTER VI: Forms orthogonal to holomorphic forms. Weighted formula for solving the $overline{partial}$-equation, and applications
§21. Forms orthogonal to holomorphic forms
§22. Generalization of Theorem 8.1
§23. Weighted formula for solving the a-problem in strictly convex domains and zeros of functions of the Nevanlinna-Dzhrbashyan class
CHAPTER VII: REPRESENTATION AND MULITPLICATION OF DISTRIBUTIONS IN HIGHER DIMENSIONS
§24. Harmonic representation of distributions
§25. Multiplication of distributions and its properties
§26. Examples of products of distributions
SUPPLEMENT TO THE BRIEF HISTORICAL SURVEY
BIBLIOGRAPHY
SUBJECT INDEX
INDEX OF SYMBOLS