Integral Representations And Residues In Multidimensional Complex Analysis

Author : Lev Abramovich Aĭzenberg,Aleksandr Petrovich I︠U︡zhakov
Publisher : American Mathematical Soc.
Page : 283 pages
File Size : 50,6 Mb
Release : 1983
Category : Mathematics
ISBN : 9780821815502

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Integral Representations and Residues in Multidimensional Complex Analysis by Lev Abramovich Aĭzenberg,Aleksandr Petrovich I︠U︡zhakov Pdf

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,Simona G. Myslivets
Publisher : Springer
Page : 225 pages
File Size : 53,7 Mb
Release : 2015-09-09
Category : Mathematics
ISBN : 9783319216591

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Multidimensional Integral Representations by Alexander M. Kytmanov,Simona G. Myslivets Pdf

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 : R. Michael Range
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 55,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475719185

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Holomorphic Functions and Integral Representations in Several Complex Variables by R. Michael Range Pdf

The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.

Author : L.A. Aizenberg
Publisher : Springer
Page : 299 pages
File Size : 42,5 Mb
Release : 2011-10-21
Category : Mathematics
ISBN : 9401115974

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Carleman’s Formulas in Complex Analysis by L.A. Aizenberg Pdf

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).

Author : Alekos Vidras,Alain Yger
Publisher : American Mathematical Society
Page : 556 pages
File Size : 49,5 Mb
Release : 2023-10-18
Category : Mathematics
ISBN : 9781470471125

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Multidimensional Residue Theory and Applications by Alekos Vidras,Alain Yger Pdf

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 : Boris Vladimirovich Shabat
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 40,5 Mb
Release : 1992-11-04
Category : Mathematics
ISBN : 9780821819753

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Introduction to Complex Analysis by Boris Vladimirovich Shabat Pdf

Since the 1960s, there has been a flowering in higher-dimensional complex analysis. Both classical and new results in this area have found numerous applications in analysis, differential and algebraic geometry, and, in particular, contemporary mathematical physics. In many areas of modern mathematics, the mastery of the foundations of higher-dimensional complex analysis has become necessary for any specialist. Intended as a first study of higher-dimensional complex analysis, this book covers the theory of holomorphic functions of several complex variables, holomorphic mappings, and submanifolds of complex Euclidean space.

Author : L.A. Aizenberg
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401115964

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Carleman’s Formulas in Complex Analysis by L.A. Aizenberg Pdf

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).

Author : E.M. Chirka,A.G. Vitushkin,P. Dolbeault,G.M. Khenkin
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642615252

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Introduction to Complex Analysis by E.M. Chirka,A.G. Vitushkin,P. Dolbeault,G.M. Khenkin Pdf

From the reviews: "... In sum, the volume under review is the first quarter of an important work that surveys an active branch of modern mathematics. Some of the individual articles are reminiscent in style of the early volumes of the first Ergebnisse series and will probably prove to be equally useful as a reference; ...for the appropriate reader, they will be valuable sources of information about modern complex analysis." Bulletin of the Am.Math.Society, 1991 "... This remarkable book has a helpfully informal style, abundant motivation, outlined proofs followed by precise references, and an extensive bibliography; it will be an invaluable reference and a companion to modern courses on several complex variables." ZAMP, Zeitschrift für Angewandte Mathematik und Physik, 1990

Author : G.M. Khenkin,A.G. Vitushkin
Publisher : Springer Science & Business Media
Page : 267 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642578823

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Several Complex Variables II by G.M. Khenkin,A.G. Vitushkin Pdf

Plurisubharmonic functions playa major role in the theory of functions of several complex variables. The extensiveness of plurisubharmonic functions, the simplicity of their definition together with the richness of their properties and. most importantly, their close connection with holomorphic functions have assured plurisubharmonic functions a lasting place in multidimensional complex analysis. (Pluri)subharmonic functions first made their appearance in the works of Hartogs at the beginning of the century. They figure in an essential way, for example, in the proof of the famous theorem of Hartogs (1906) on joint holomorphicity. Defined at first on the complex plane IC, the class of subharmonic functions became thereafter one of the most fundamental tools in the investigation of analytic functions of one or several variables. The theory of subharmonic functions was developed and generalized in various directions: subharmonic functions in Euclidean space IRn, plurisubharmonic functions in complex space en and others. Subharmonic functions and the foundations ofthe associated classical poten tial theory are sufficiently well exposed in the literature, and so we introduce here only a few fundamental results which we require. More detailed expositions can be found in the monographs of Privalov (1937), Brelot (1961), and Landkof (1966). See also Brelot (1972), where a history of the development of the theory of subharmonic functions is given.

Author : Stancho Dimiev,Kouei Sekigawa
Publisher : World Scientific
Page : 382 pages
File Size : 40,7 Mb
Release : 1999-09-17
Category : Mathematics
ISBN : 9789814543750

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Aspects Of Complex Analysis, Differential Geometry, Mathematical Physics And Applications - Proceedings Of The Fourth International Workshop On Complex Structures And Vector Fields by Stancho Dimiev,Kouei Sekigawa Pdf

This volume constitutes the proceedings of a workshop whose main purpose was to exchange information on current topics in complex analysis, differential geometry, mathematical physics and applications, and to group aspects of new mathematics.

Author : Zair Ibragimov,Norman Levenberg,Sergey Pinchuk,Azimbay Sadullaev
Publisher : American Mathematical Soc.
Page : 168 pages
File Size : 47,7 Mb
Release : 2016-04-21
Category : Functional analysis
ISBN : 9781470419271

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Topics in Several Complex Variables by Zair Ibragimov,Norman Levenberg,Sergey Pinchuk,Azimbay Sadullaev Pdf

This volume contains the proceedings of the Special Session on Several Complex Variables, which was held during the first USA-Uzbekistan Conference on Analysis and Mathematical Physics from May 20–23, 2014, at California State University, Fullerton. This volume covers a wide variety of topics in pluripotential theory, symplectic geometry and almost complex structures, integral formulas, holomorphic extension, and complex dynamics. In particular, the reader will find articles on Lagrangian submanifolds and rational convexity, multidimensional residues, S-parabolic Stein manifolds, Segre varieties, and the theory of quasianalytic functions.

Author : I︠U︡riĭ Pitrimovich Razmyslov
Publisher : American Mathematical Soc.
Page : 468 pages
File Size : 48,5 Mb
Release : 1994
Category : Mathematics
ISBN : 0821846086

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Identities of Algebras and their Representations by I︠U︡riĭ Pitrimovich Razmyslov Pdf

During the past forty years, a new trend in the theory of associative algebras, Lie algebras, and their representations has formed under the influence of mathematical logic and universal algebra, namely, the theory of varieties and identities of associative algebras, Lie algebras, and their representations. The last twenty years have seen the creation of the method of 2-words and *a-functions, which allowed a number of problems in the theory of groups, rings, Lie algebras, and their representations to be solved in a unified way. The possibilities of this method are far from exhausted. This book sums up the applications of the method of 2-words and *a-functions in the theory of varieties and gives a systematic exposition of contemporary achievements in the theory of identities of algebras and their representations closely related to this method. The aim is to make these topics accessible to a wider group of mathematicians.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 549 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401512350

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Author : Anonim
Publisher : Unknown
Page : 792 pages
File Size : 46,8 Mb
Release : 1989
Category : Functions of complex variables
ISBN : UCAL:B4342536

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Reviews in Complex Analysis, 1980-86 by Anonim Pdf

Author : Chung-Chun Yang,Sheng Gong
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 45,9 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821851647

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Several Complex Variables in China by Chung-Chun Yang,Sheng Gong Pdf

Today, there is increasing interest in complex geometry, geometric function theory, and integral representation theory of several complex variables. The present collection of survey and research articles comprises a current overview of research in several complex variables in China. Among the topics covered are singular integrals, function spaces, differential operators, and factorization of meromorphic functions in several complex variables via analytic or geometric methods. Some results are reported in English for the first time.