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| Author | : I.A. Aizenberg |
| Publisher | : |
| Total Pages | : 283 |
| Release | : 1983 |
| Genre | : |
| ISBN | : |
| Author | : Lev Abramovich Aĭzenberg |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 296 |
| Release | : 1983 |
| Genre | : Mathematics |
| ISBN | : 0821815504 |
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.
| Author | : Alexander M. Kytmanov |
| Publisher | : |
| Total Pages | : |
| Release | : 2015 |
| Genre | : |
| ISBN | : 9783319216607 |
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
| Author | : Alexander M. Kytmanov |
| Publisher | : Springer |
| Total Pages | : 236 |
| Release | : 2015-09-09 |
| Genre | : Mathematics |
| ISBN | : 3319216597 |
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.
| Author | : A. O. Gogolin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 291 |
| Release | : 2013-10-22 |
| Genre | : Science |
| ISBN | : 3319002120 |
The theory of complex functions is a strikingly beautiful and powerful area of mathematics. Some particularly fascinating examples are seemingly complicated integrals which are effortlessly computed after reshaping them into integrals along contours, as well as apparently difficult differential and integral equations, which can be elegantly solved using similar methods. To use them is sometimes routine but in many cases it borders on an art. The goal of the book is to introduce the reader to this beautiful area of mathematics and to teach him or her how to use these methods to solve a variety of problems ranging from computation of integrals to solving difficult integral equations. This is done with a help of numerous examples and problems with detailed solutions.
| Author | : Alekos Vidras |
| Publisher | : American Mathematical Society |
| Total Pages | : 556 |
| Release | : 2023-10-18 |
| Genre | : Mathematics |
| ISBN | : 1470471124 |
Residue theory is an active area of complex analysis with connections and applications to fields as diverse as partial differential and integral equations, computer algebra, arithmetic or diophantine geometry, and mathematical physics. Multidimensional Residue Theory and Applications defines and studies multidimensional residues via analytic continuation for holomorphic bundle-valued current maps. This point of view offers versatility and flexibility to the tools and constructions proposed, allowing these residues to be defined and studied outside the classical case of complete intersection. The book goes on to show how these residues are algebraic in nature, and how they relate and apply to a wide range of situations, most notably to membership problems, such as the Briançon–Skoda theorem and Hilbert's Nullstellensatz, to arithmetic intersection theory and to tropical geometry. This book will supersede the existing literature in this area, which dates back more than three decades. It will be appreciated by mathematicians and graduate students in multivariate complex analysis. But thanks to the gentle treatment of the one-dimensional case in Chapter 1 and the rich background material in the appendices, it may also be read by specialists in arithmetic, diophantine, or tropical geometry, as well as in mathematical physics or computer algebra.
| Author | : A. K. T͡Sikh |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 187 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : 9780821845608 |
The technique of residues is known for its many applications in different branches of mathematics. Tsikh's book presents a systematic account of residues associated with holomorphic mappings and indicates many applications. The book begins with preliminaries from the theory of analytic sets, together with material from algebraic topology that is necessary for the integration of differential forms over chains. Tsikh then presents a detailed study of residues associated with mappings that preserve dimension (local residues). Local residues are applied to algebraic geometry and to problems connected with the investigation and calculation of double series and integrals. There is also a treatment of residues associated with mappings that reduce dimension - that is, residues of semimeromorphic forms, connected with integration over tubes around nondiscrete analytic sets.
| Author | : Reynaldo Rocha-Chavez |
| Publisher | : CRC Press |
| Total Pages | : 217 |
| Release | : 2001-08-03 |
| Genre | : Mathematics |
| ISBN | : 1420035517 |
The theory of holomorphic functions of several complex variables emerged from the attempt to generalize the theory in one variable to the multidimensional situation. Research in this area has led to the discovery of many sophisticated facts, structures, ideas, relations, and applications. This deepening of knowledge, however, has also revealed more
| Author | : Reynaldo Rocha-Chavez |
| Publisher | : Chapman and Hall/CRC |
| Total Pages | : 216 |
| Release | : 2001-08-03 |
| Genre | : Mathematics |
| ISBN | : 9781584882466 |
The theory of holomorphic functions of several complex variables emerged from the attempt to generalize the theory in one variable to the multidimensional situation. Research in this area has led to the discovery of many sophisticated facts, structures, ideas, relations, and applications. This deepening of knowledge, however, has also revealed more and more paradoxical differences between the structures of the two theories. The authors of this Research Note were driven by the quest to construct a theory in several complex variables that has the same structure as the one-variable theory. That is, they sought a reproducing kernel for the whole class that is universal and from same class. Integral Theorems for Functions and Differential Forms in Cm documents their success. Their highly original approach allowed them to obtain new results and refine some well-known results from the classical theory of several complex variables. The 'hyperholomorphic" theory they developed proved to be a kind of direct sum of function theories for two Dirac-type operators of Clifford analysis considered in the same domain. In addition to new results and methods, this work presents a first-look at a brand new setting, based upon the natural language of differential forms, for complex analysis. Integral Theorems for Functions and Differential Forms in Cm reveals a deep link between the fields of several complex variables theory and Clifford analysis. It will have a strong influence on researchers in both areas, and undoubtedly will change the general viewpoint on the methods and ideas of several complex variables theory.
| Author | : Alexey Karapetyants |
| Publisher | : Springer Nature |
| Total Pages | : 475 |
| Release | : 2019-08-28 |
| Genre | : Mathematics |
| ISBN | : 3030267482 |
This proceedings volume gathers selected, peer-reviewed papers from the "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis VIII" (OTHA 2018) conference, which was held in Rostov-on-Don, Russia, in April 2018. The book covers a diverse range of topics in advanced mathematics, including harmonic analysis, functional analysis, operator theory, function theory, differential equations and fractional analysis – all fields that have been intensively developed in recent decades. Direct and inverse problems arising in mathematical physics are studied and new methods for solving them are presented. Complex multiparameter objects that require the involvement of operators with variable parameters and functional spaces, with fractional and even variable exponents, make these approaches all the more relevant. Given its scope, the book will especially benefit researchers with an interest in new trends in harmonic analysis and operator theory, though it will also appeal to graduate students seeking new and intriguing topics for further investigation.
