Multidimensional Integral Representations

by Alexander M. Kytmanov (Author), Simona G. Myslivets (Author)
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

From the Back Cover
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.

Topics
Several Complex Variables and Analytic Spaces