Multidimensional Integral Representations Problems of Analytic Continuation [Paperback]

The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappi?, 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.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.

The monograph is essentially self-contained, requiring knowledge only of the contents of a basic course in several complex variables, this making it suitable for a graduate students seminar and independent study. The material is well organized and its presentation is lucid. (Alekos Vidras, Mathematical Reviews, July, 2016)

The monograph is based on recent results obtained by the authors. & The monograph will be useful to graduate students, PhD students, and researchers in function theory of several complex variables. (Marek Jarnicki, zbMATH 1341.32001, 2016)

The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantal³n