Multidimensional Integral Representations

Problems of Analytic Continuation

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis
Cover of the book Multidimensional Integral Representations by Simona G. Myslivets, Alexander M. Kytmanov, Springer International Publishing
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Author: Simona G. Myslivets, Alexander M. Kytmanov ISBN: 9783319216591
Publisher: Springer International Publishing Publication: September 9, 2015
Imprint: Springer Language: English
Author: Simona G. Myslivets, Alexander M. Kytmanov
ISBN: 9783319216591
Publisher: Springer International Publishing
Publication: September 9, 2015
Imprint: Springer
Language: English

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.

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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.

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