Integral Representations

Author : R. Michael Range
Publisher : Springer Science & Business Media
ISBN 13 : 1475719183
Total Pages : 405 pages
Book Rating : 4.85/5 ( download)

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Download or read book Holomorphic Functions and Integral Representations in Several Complex Variables written by R. Michael Range and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : I. Reiner
Publisher : Springer
ISBN 13 : 3540350071
Total Pages : 284 pages
Book Rating : 4.71/5 ( download)

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Download or read book Integral Representations written by I. Reiner and published by Springer. This book was released on 2006-11-15 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Alexander M. Kytmanov
Publisher : Springer
ISBN 13 : 3319216597
Total Pages : 225 pages
Book Rating : 4.91/5 ( download)

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Download or read book Multidimensional Integral Representations written by Alexander M. Kytmanov and published by Springer. This book was released on 2015-09-09 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Klaus W. Roggenkamp
Publisher : Springer
ISBN 13 : 3540387897
Total Pages : 490 pages
Book Rating : 4.93/5 ( download)

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Download or read book Integral Representations and Applications written by Klaus W. Roggenkamp and published by Springer. This book was released on 2006-11-14 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Lev Abramovich Aĭzenberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821815504
Total Pages : 296 pages
Book Rating : 4.02/5 ( download)

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Download or read book Integral Representations and Residues in Multidimensional Complex Analysis written by Lev Abramovich Aĭzenberg and published by American Mathematical Soc.. This book was released on 1983 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Vladislav V Kravchenko
Publisher : CRC Press
ISBN 13 : 1000115291
Total Pages : 256 pages
Book Rating : 4.91/5 ( download)

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Download or read book Integral Representations For Spatial Models of Mathematical Physics written by Vladislav V Kravchenko and published by CRC Press. This book was released on 2020-11-25 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a new mathematical theory for the treatment of an ample series of spatial problems of electrodynamics, particle physics, quantum mechanics and elasticity theory. This technique proves to be as powerful for solving the spatial problems of mathematical physics as complex analysis is for solving planar problems. The main analytic tool of the book, a non-harmonic version of hypercomplex analysis recently developed by the authors, is presented in detail. There are given applications of this theory to the boundary value problems of electrodynamics and elasticity theory as well as to the problem of quark confinement. A new approach to the linearization of special classes of the self-duality equation is also considered. Detailed proofs are given throughout. The book contains an extensive bibliography on closely related topics. This book will be of particular interest to academic and professional specialists and students in mathematics and physics who are interested in integral representations for partial differential equations. The book is self-contained and could be used as a main reference for special course seminars on the subject.

Author : R. Michael Range
Publisher : Springer Science & Business Media
ISBN 13 : 9780387962597
Total Pages : 424 pages
Book Rating : 4.9X/5 ( download)

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Download or read book Holomorphic Functions and Integral Representations in Several Complex Variables written by R. Michael Range and published by Springer Science & Business Media. This book was released on 1998-06-26 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Richard C. MacCamy
Publisher :
ISBN 13 :
Total Pages : 62 pages
Book Rating : 4.75/5 ( download)

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Download or read book Integral Representations of Axially Symmetric Potential Functions written by Richard C. MacCamy and published by . This book was released on 1960 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Soren Rasmussen
Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.14/5 ( download)

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Download or read book Non-linear Semi-groups Evolution Equations and Product-integral Representations written by Soren Rasmussen and published by . This book was released on 1971 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Vladislav V Kravchenko
Publisher : CRC Press
ISBN 13 : 1000158098
Total Pages : 258 pages
Book Rating : 4.90/5 ( download)

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Download or read book Integral Representations For Spatial Models of Mathematical Physics written by Vladislav V Kravchenko and published by CRC Press. This book was released on 2020-11-26 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a new mathematical theory for the treatment of an ample series of spatial problems of electrodynamics, particle physics, quantum mechanics and elasticity theory. This technique proves to be as powerful for solving the spatial problems of mathematical physics as complex analysis is for solving planar problems. The main analytic tool of the book, a non-harmonic version of hypercomplex analysis recently developed by the authors, is presented in detail. There are given applications of this theory to the boundary value problems of electrodynamics and elasticity theory as well as to the problem of quark confinement. A new approach to the linearization of special classes of the self-duality equation is also considered. Detailed proofs are given throughout. The book contains an extensive bibliography on closely related topics. This book will be of particular interest to academic and professional specialists and students in mathematics and physics who are interested in integral representations for partial differential equations. The book is self-contained and could be used as a main reference for special course seminars on the subject.