Cr Manifolds And The Tangential Cauchy Riemann Complex

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CR Manifolds and the Tangential Cauchy Riemann Complex

Author : Al Boggess
Publisher : Routledge
ISBN 13 : 1351457578
Total Pages : 386 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis CR Manifolds and the Tangential Cauchy Riemann Complex by : Al Boggess

Download or read book CR Manifolds and the Tangential Cauchy Riemann Complex written by Al Boggess and published by Routledge. This book was released on 2017-09-20 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: CR Manifolds and the Tangential Cauchy Riemann Complex provides an elementary introduction to CR manifolds and the tangential Cauchy-Riemann Complex and presents some of the most important recent developments in the field. The first half of the book covers the basic definitions and background material concerning CR manifolds, CR functions, the tangential Cauchy-Riemann Complex and the Levi form. The second half of the book is devoted to two significant areas of current research. The first area is the holomorphic extension of CR functions. Both the analytic disc approach and the Fourier transform approach to this problem are presented. The second area of research is the integral kernal approach to the solvability of the tangential Cauchy-Riemann Complex. CR Manifolds and the Tangential Cauchy Riemann Complex will interest students and researchers in the field of several complex variable and partial differential equations.

Differential Geometry and Analysis on CR Manifolds

Author : Sorin Dragomir
Publisher : Springer Science & Business Media
ISBN 13 : 0817644830
Total Pages : 499 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Differential Geometry and Analysis on CR Manifolds by : Sorin Dragomir

Download or read book Differential Geometry and Analysis on CR Manifolds written by Sorin Dragomir and published by Springer Science & Business Media. This book was released on 2007-06-10 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form Explains how certain results from analysis are employed in CR geometry Many examples and explicitly worked-out proofs of main geometric results in the first section of the book making it suitable as a graduate main course or seminar textbook Provides unproved statements and comments inspiring further study

Partial Differential Equations in Several Complex Variables

Author : So-chin Chen
Publisher : American Mathematical Soc.
ISBN 13 : 9780821829615
Total Pages : 396 pages
Book Rating : 4.8/5 (296 download)

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Book Synopsis Partial Differential Equations in Several Complex Variables by : So-chin Chen

Download or read book Partial Differential Equations in Several Complex Variables written by So-chin Chen and published by American Mathematical Soc.. This book was released on 2001 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as both an introductory text and a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few decades, significant progress has been made in the study of Cauchy-Riemann and tangential Cauchy-Riemann operators; this progress greatly influenced the development of PDEs and several complex variables. After the background material in complex analysis is developed in Chapters 1 to 3, thenext three chapters are devoted to the solvability and regularity of the Cauchy-Riemann equations using Hilbert space techniques. The authors provide a systematic study of the Cauchy-Riemann equations and the \bar\partial-Neumann problem, including Hórmander's L2 existence progress on the globalregularity and irregularity of the \bar\partial-Neumann operators. The second part of the book gives a comprehensive study of the tangential Cauchy-Riemann equations, another important class of equations in several complex variables first studied by Lewy. An up-to-date account of the L2 theory for \bar\partial b operator is given. Explicit integral solution representations are constructed both on the Heisenberg groups and on strictly convex boundaries with estimates in Hölder and L2spaces. Embeddability of abstract CR structures is discussed in detail here for the first time.Titles in this series are co-published with International Press, Cambridge, MA.

Real Submanifolds in Complex Space and Their Mappings (PMS-47)

Author : M. Salah Baouendi
Publisher : Princeton University Press
ISBN 13 : 1400883962
Total Pages : 418 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Real Submanifolds in Complex Space and Their Mappings (PMS-47) by : M. Salah Baouendi

Download or read book Real Submanifolds in Complex Space and Their Mappings (PMS-47) written by M. Salah Baouendi and published by Princeton University Press. This book was released on 2016-06-02 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents many of the main developments of the past two decades in the study of real submanifolds in complex space, providing crucial background material for researchers and advanced graduate students. The techniques in this area borrow from real and complex analysis and partial differential equations, as well as from differential, algebraic, and analytical geometry. In turn, these latter areas have been enriched over the years by the study of problems in several complex variables addressed here. The authors, M. Salah Baouendi, Peter Ebenfelt, and Linda Preiss Rothschild, include extensive preliminary material to make the book accessible to nonspecialists. One of the most important topics that the authors address here is the holomorphic extension of functions and mappings that satisfy the tangential Cauchy-Riemann equations on real submanifolds. They present the main results in this area with a novel and self-contained approach. The book also devotes considerable attention to the study of holomorphic mappings between real submanifolds, and proves finite determination of such mappings by their jets under some optimal assumptions. The authors also give a thorough comparison of the various nondegeneracy conditions for manifolds and mappings and present new geometric interpretations of these conditions. Throughout the book, Cauchy-Riemann vector fields and their orbits play a central role and are presented in a setting that is both general and elementary.

Calculus on Heisenberg Manifolds

Author : Richard Beals
Publisher : Princeton University Press
ISBN 13 : 9780691085012
Total Pages : 212 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Calculus on Heisenberg Manifolds by : Richard Beals

Download or read book Calculus on Heisenberg Manifolds written by Richard Beals and published by Princeton University Press. This book was released on 1988-08-21 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Calculus on Heisenberg Manifolds. (AM-119), Volume 119, will be forthcoming.

The Neumann Problem for the Cauchy-Riemann Complex. (AM-75), Volume 75

Author : Gerald B. Folland
Publisher : Princeton University Press
ISBN 13 : 1400881528
Total Pages : 156 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis The Neumann Problem for the Cauchy-Riemann Complex. (AM-75), Volume 75 by : Gerald B. Folland

Download or read book The Neumann Problem for the Cauchy-Riemann Complex. (AM-75), Volume 75 written by Gerald B. Folland and published by Princeton University Press. This book was released on 2016-03-02 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part explanation of important recent work, and part introduction to some of the techniques of modern partial differential equations, this monograph is a self-contained exposition of the Neumann problem for the Cauchy-Riemann complex and certain of its applications. The authors prove the main existence and regularity theorems in detail, assuming only a knowledge of the basic theory of differentiable manifolds and operators on Hilbert space. They discuss applications to the theory of several complex variables, examine the associated complex on the boundary, and outline other techniques relevant to these problems. In an appendix they develop the functional analysis of differential operators in terms of Sobolev spaces, to the extent it is required for the monograph.

Geometry of Cauchy-Riemann Submanifolds

Author : Sorin Dragomir
Publisher : Springer
ISBN 13 : 9811009163
Total Pages : 402 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Geometry of Cauchy-Riemann Submanifolds by : Sorin Dragomir

Download or read book Geometry of Cauchy-Riemann Submanifolds written by Sorin Dragomir and published by Springer. This book was released on 2016-05-31 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic recast of the tangential Cauchy–Riemann equations in complex analysis involving several complex variables. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds. Intended as a tribute to Professor Aurel Bejancu, who discovered the notion of a CR submanifold of a Hermitian manifold in 1978, the book provides an up-to-date overview of several topics in the geometry of CR submanifolds. Presenting detailed information on the most recent advances in the area, it represents a useful resource for mathematicians and physicists alike.

Tasty Bits of Several Complex Variables

Author : Jiri Lebl
Publisher : Lulu.com
ISBN 13 : 1365095576
Total Pages : 142 pages
Book Rating : 4.3/5 (65 download)

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Book Synopsis Tasty Bits of Several Complex Variables by : Jiri Lebl

Download or read book Tasty Bits of Several Complex Variables written by Jiri Lebl and published by Lulu.com. This book was released on 2016-05-05 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014 and Spring 2016 semester at Oklahoma State University. The course covers basics of holomorphic function theory, CR geometry, the dbar problem, integral kernels and basic theory of complex analytic subvarieties. See http: //www.jirka.org/scv/ for more information.

Foliations in Cauchy-Riemann Geometry

Author : Elisabetta Barletta
Publisher : American Mathematical Soc.
ISBN 13 : 0821843044
Total Pages : 270 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Foliations in Cauchy-Riemann Geometry by : Elisabetta Barletta

Download or read book Foliations in Cauchy-Riemann Geometry written by Elisabetta Barletta and published by American Mathematical Soc.. This book was released on 2007 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the relationship between foliation theory and differential geometry and analysis on Cauchy-Riemann (CR) manifolds. The main objects of study are transversally and tangentially CR foliations, Levi foliations of CR manifolds, solutions of the Yang-Mills equations, tangentially Monge-Ampere foliations, the transverse Beltrami equations, and CR orbifolds. The novelty of the authors' approach consists in the overall use of the methods of foliation theory and choice of specific applications. Examples of such applications are Rea's holomorphic extension of Levi foliations, Stanton's holomorphic degeneracy, Boas and Straube's approximately commuting vector fields method for the study of global regularity of Neumann operators and Bergman projections in multi-dimensional complex analysis in several complex variables, as well as various applications to differential geometry. Many open problems proposed in the monograph may attract the mathematical community and lead to further applications of

Function Theory of Several Complex Variables

Author : Steven George Krantz
Publisher : American Mathematical Soc.
ISBN 13 : 0821827243
Total Pages : 586 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Function Theory of Several Complex Variables by : Steven George Krantz

Download or read book Function Theory of Several Complex Variables written by Steven George Krantz and published by American Mathematical Soc.. This book was released on 2001 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.

Elementary Introduction to the Theory of Pseudodifferential Operators

Author : Xavier Saint Raymond
Publisher : Routledge
ISBN 13 : 1351452932
Total Pages : 120 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Elementary Introduction to the Theory of Pseudodifferential Operators by : Xavier Saint Raymond

Download or read book Elementary Introduction to the Theory of Pseudodifferential Operators written by Xavier Saint Raymond and published by Routledge. This book was released on 2018-02-06 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 19th century, the Fourier transformation was introduced to study various problems of partial differential equations. Since 1960, this old tool has been developed into a well-organized theory called microlocal analysis that is based on the concept of the pseudo-differential operator. This book provides the fundamental knowledge non-specialists need in order to use microlocal analysis. It is strictly mathematical in the sense that it contains precise definitions, statements of theorems and complete proofs, and follows the usual method of pure mathematics. The book explains the origin of the theory (i.e., Fourier transformation), presents an elementary construcion of distribution theory, and features a careful exposition of standard pseudodifferential theory. Exercises, historical notes, and bibliographical references are included to round out this essential book for mathematics students; engineers, physicists, and mathematicians who use partial differential equations; and advanced mathematics instructors.

Modern Differential Geometry of Curves and Surfaces with Mathematica

Author : Elsa Abbena
Publisher : CRC Press
ISBN 13 : 1351992201
Total Pages : 1024 pages
Book Rating : 4.3/5 (519 download)

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Book Synopsis Modern Differential Geometry of Curves and Surfaces with Mathematica by : Elsa Abbena

Download or read book Modern Differential Geometry of Curves and Surfaces with Mathematica written by Elsa Abbena and published by CRC Press. This book was released on 2017-09-06 with total page 1024 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray’s famous textbook, covers how to define and compute standard geometric functions using Mathematica for constructing new curves and surfaces from existing ones. Since Gray’s death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they reorganized the material to provide a clearer division between the text and the Mathematica code and added a Mathematica notebook as an appendix to each chapter. They also address important new topics, such as quaternions. The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi’s formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but Mathematica handles it easily, either through computations or through graphing curvature. Another part of Mathematica that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted. Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use Mathematica to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples. It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.

Wavelets

Author : John J. Benedetto
Publisher : CRC Press
ISBN 13 : 1000443469
Total Pages : 586 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Wavelets by : John J. Benedetto

Download or read book Wavelets written by John J. Benedetto and published by CRC Press. This book was released on 2021-07-28 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelets is a carefully organized and edited collection of extended survey papers addressing key topics in the mathematical foundations and applications of wavelet theory. The first part of the book is devoted to the fundamentals of wavelet analysis. The construction of wavelet bases and the fast computation of the wavelet transform in both continuous and discrete settings is covered. The theory of frames, dilation equations, and local Fourier bases are also presented. The second part of the book discusses applications in signal analysis, while the third part covers operator analysis and partial differential equations. Each chapter in these sections provides an up-to-date introduction to such topics as sampling theory, probability and statistics, compression, numerical analysis, turbulence, operator theory, and harmonic analysis. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. It will be an especially useful reference for harmonic analysts, partial differential equation researchers, signal processing engineers, numerical analysts, fluids researchers, and applied mathematicians.

Harmonic Analysis and Applications

Author : John J. Benedetto
Publisher : CRC Press
ISBN 13 : 1000099083
Total Pages : 357 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Harmonic Analysis and Applications by : John J. Benedetto

Download or read book Harmonic Analysis and Applications written by John J. Benedetto and published by CRC Press. This book was released on 2020-12-17 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic analysis plays an essential role in understanding a host of engineering, mathematical, and scientific ideas. In Harmonic Analysis and Applications, the analysis and synthesis of functions in terms of harmonics is presented in such a way as to demonstrate the vitality, power, elegance, usefulness, and the intricacy and simplicity of the subject. This book is about classical harmonic analysis - a textbook suitable for students, and an essay and general reference suitable for mathematicians, physicists, and others who use harmonic analysis. Throughout the book, material is provided for an upper level undergraduate course in harmonic analysis and some of its applications. In addition, the advanced material in Harmonic Analysis and Applications is well-suited for graduate courses. The course is outlined in Prologue I. This course material is excellent, not only for students, but also for scientists, mathematicians, and engineers as a general reference. Chapter 1 covers the Fourier analysis of integrable and square integrable (finite energy) functions on R. Chapter 2 of the text covers distribution theory, emphasizing the theory's useful vantage point for dealing with problems and general concepts from engineering, physics, and mathematics. Chapter 3 deals with Fourier series, including the Fourier analysis of finite and infinite sequences, as well as functions defined on finite intervals. The mathematical presentation, insightful perspectives, and numerous well-chosen examples and exercises in Harmonic Analysis and Applications make this book well worth having in your collection.

Fast Fourier Transforms

Author : James S. Walker
Publisher : CRC Press
ISBN 13 : 1351448889
Total Pages : 464 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Fast Fourier Transforms by : James S. Walker

Download or read book Fast Fourier Transforms written by James S. Walker and published by CRC Press. This book was released on 2017-11-22 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of an indispensable text provides a clear treatment of Fourier Series, Fourier Transforms, and FFTs. The unique software, included with the book and newly updated for this edition, allows the reader to generate, firsthand, images of all aspects of Fourier analysis described in the text. Topics covered include :

Clifford Algebras in Analysis and Related Topics

Author : John Ryan
Publisher : CRC Press
ISBN 13 : 1351460285
Total Pages : 384 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Clifford Algebras in Analysis and Related Topics by : John Ryan

Download or read book Clifford Algebras in Analysis and Related Topics written by John Ryan and published by CRC Press. This book was released on 2018-03-09 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book contains the most up-to-date and focused description of the applications of Clifford algebras in analysis, particularly classical harmonic analysis. It is the first single volume devoted to applications of Clifford analysis to other aspects of analysis. All chapters are written by world authorities in the area. Of particular interest is the contribution of Professor Alan McIntosh. He gives a detailed account of the links between Clifford algebras, monogenic and harmonic functions and the correspondence between monogenic functions and holomorphic functions of several complex variables under Fourier transforms. He describes the correspondence between algebras of singular integrals on Lipschitz surfaces and functional calculi of Dirac operators on these surfaces. He also discusses links with boundary value problems over Lipschitz domains. Other specific topics include Hardy spaces and compensated compactness in Euclidean space; applications to acoustic scattering and Galerkin estimates; scattering theory for orthogonal wavelets; applications of the conformal group and Vahalen matrices; Newmann type problems for the Dirac operator; plus much, much more! Clifford Algebras in Analysis and Related Topics also contains the most comprehensive section on open problems available. The book presents the most detailed link between Clifford analysis and classical harmonic analysis. It is a refreshing break from the many expensive and lengthy volumes currently found on the subject.

Invariance Theory

Author : Peter B. Gilkey
Publisher : CRC Press
ISBN 13 : 9780849378744
Total Pages : 534 pages
Book Rating : 4.3/5 (787 download)

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Book Synopsis Invariance Theory by : Peter B. Gilkey

Download or read book Invariance Theory written by Peter B. Gilkey and published by CRC Press. This book was released on 1994-12-22 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.