Multidimensional Integral Representations

The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappiè, Koppelman, multidimensional logarithmic residue etc., and their boundary properties. The applications considered are problems of analytic continuation of functions from the boundary of a bounded domain in C^n. In contrast to the well-known Hartogs-Bochner theorem, this book investigates functions with the one-dimensional property of holomorphic extension along complex lines, and includes the problems of receiving multidimensional boundary analogs of the Morera theorem. This book is a valuable resource for specialists in complex analysis, theoretical physics, as well as graduate and postgraduate students with an understanding of standard university courses in complex, real and functional analysis, as well as algebra and geometry.

Summarizes recent results on integral representations and residues Includes studies on different families of complex lines and curves sufficient for holomorphic continuation of functions from the boundary of a bounded domain Provides multidimensional logarithmic residue formulae with their boundary properties to obtain multidimensional boundary analogs of the Morera theorem

Inhalt
Preface. 1 Multidimensional Integral Representations.- 2 Properties of the Bochner-Martinelli Integral and the Logarithmic Residue Formula.- 3 On the Multidimensional Boundary Analogue of the Morera Theorem.- 4 Functions with the One-dimensional Holomorphic Extension Property.- References.- Index.