Multidimensional Integral Representations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multidimensional Integral Representations write by Alexander M. Kytmanov. This book was released on 2015-09-09. Multidimensional Integral Representations available in PDF, EPUB and Kindle. 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.
Integral Representations and Residues in Multidimensional Complex Analysis
Integral Representations and Residues in Multidimensional Complex Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Integral Representations and Residues in Multidimensional Complex Analysis write by Lev Abramovich Aĭzenberg. This book was released on 1983. Integral Representations and Residues in Multidimensional Complex Analysis available in PDF, EPUB and Kindle. This book deals with integral representations of holomorphic functions of several complex variables, the multidimensional logarithmic residue, and the theory of multidimensional residues. Applications are given to implicit function theory, systems of nonlinear equations, computation of the multiplicity of a zero of a mapping, and computation of combinatorial sums in closed form. Certain applications in multidimensional complex analysis are considered. The monograph is intended for specialists in theoretical and applied mathematics and theoretical physics, and for postgraduate and graduate students interested in multidimensional complex analysis or its applications.
Multidimensional Integral Representations
Multidimensional Integral Representations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multidimensional Integral Representations write by Alexander M. Kytmanov. This book was released on 2016-10-22. Multidimensional Integral Representations available in PDF, EPUB and Kindle. 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.
The Bochner-Martinelli Integral and Its Applications
The Bochner-Martinelli Integral and Its Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Bochner-Martinelli Integral and Its Applications write by Alexander M. Kytmanov. This book was released on 2012-12-06. The Bochner-Martinelli Integral and Its Applications available in PDF, EPUB and Kindle. The Bochner-Martinelli integral representation for holomorphic functions or'sev eral complex variables (which has already become classical) appeared in the works of Martinelli and Bochner at the beginning of the 1940's. It was the first essen tially multidimensional representation in which the integration takes place over the whole boundary of the domain. This integral representation has a universal 1 kernel (not depending on the form of the domain), like the Cauchy kernel in e . However, in en when n > 1, the Bochner-Martinelli kernel is harmonic, but not holomorphic. For a long time, this circumstance prevented the wide application of the Bochner-Martinelli integral in multidimensional complex analysis. Martinelli and Bochner used their representation to prove the theorem of Hartogs (Osgood Brown) on removability of compact singularities of holomorphic functions in en when n > 1. In the 1950's and 1960's, only isolated works appeared that studied the boundary behavior of Bochner-Martinelli (type) integrals by analogy with Cauchy (type) integrals. This study was based on the Bochner-Martinelli integral being the sum of a double-layer potential and the tangential derivative of a single-layer potential. Therefore the Bochner-Martinelli integral has a jump that agrees with the integrand, but it behaves like the Cauchy integral under approach to the boundary, that is, somewhat worse than the double-layer potential. Thus, the Bochner-Martinelli integral combines properties of the Cauchy integral and the double-layer potential.
Carleman’s Formulas in Complex Analysis
Carleman’s Formulas in Complex Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Carleman’s Formulas in Complex Analysis write by L.A. Aizenberg. This book was released on 2012-12-06. Carleman’s Formulas in Complex Analysis available in PDF, EPUB and Kindle. Integral representations of holomorphic functions play an important part in the classical theory of functions of one complex variable and in multidimensional com plex analysis (in the later case, alongside with integration over the whole boundary aD of a domain D we frequently encounter integration over the Shilov boundary 5 = S(D)). They solve the classical problem of recovering at the points of a do main D a holomorphic function that is sufficiently well-behaved when approaching the boundary aD, from its values on aD or on S. Alongside with this classical problem, it is possible and natural to consider the following one: to recover the holomorphic function in D from its values on some set MeaD not containing S. Of course, M is to be a set of uniqueness for the class of holomorphic functions under consideration (for example, for the functions continuous in D or belonging to the Hardy class HP(D), p ~ 1).
