Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 0817644407
Category : Mathematics
Languages : en
Pages : 311
Book Description
* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations
Geometric Function Theory
Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 0817644407
Category : Mathematics
Languages : en
Pages : 311
Book Description
* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations
Publisher: Springer Science & Business Media
ISBN: 0817644407
Category : Mathematics
Languages : en
Pages : 311
Book Description
* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations
Function Theory of Several Complex Variables
Author: Steven George Krantz
Publisher: American Mathematical Soc.
ISBN: 0821827243
Category : Functions of several complex variables
Languages : en
Pages : 586
Book Description
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.
Publisher: American Mathematical Soc.
ISBN: 0821827243
Category : Functions of several complex variables
Languages : en
Pages : 586
Book Description
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.
Geometric Theory of Functions of a Complex Variable
Author: Gennadiĭ Mikhaĭlovich Goluzin
Publisher: American Mathematical Soc.
ISBN: 9780821886557
Category : Functions of complex variables
Languages : en
Pages : 690
Book Description
Publisher: American Mathematical Soc.
ISBN: 9780821886557
Category : Functions of complex variables
Languages : en
Pages : 690
Book Description
Handbook of Complex Analysis
Author: Reiner Kuhnau
Publisher: Elsevier
ISBN: 9780080532813
Category : Mathematics
Languages : en
Pages : 548
Book Description
Geometric Function Theory is a central part of Complex Analysis (one complex variable). The Handbook of Complex Analysis - Geometric Function Theory deals with this field and its many ramifications and relations to other areas of mathematics and physics. The theory of conformal and quasiconformal mappings plays a central role in this Handbook, for example a priori-estimates for these mappings which arise from solving extremal problems, and constructive methods are considered. As a new field the theory of circle packings which goes back to P. Koebe is included. The Handbook should be useful for experts as well as for mathematicians working in other areas, as well as for physicists and engineers. · A collection of independent survey articles in the field of GeometricFunction Theory · Existence theorems and qualitative properties of conformal and quasiconformal mappings · A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane)
Publisher: Elsevier
ISBN: 9780080532813
Category : Mathematics
Languages : en
Pages : 548
Book Description
Geometric Function Theory is a central part of Complex Analysis (one complex variable). The Handbook of Complex Analysis - Geometric Function Theory deals with this field and its many ramifications and relations to other areas of mathematics and physics. The theory of conformal and quasiconformal mappings plays a central role in this Handbook, for example a priori-estimates for these mappings which arise from solving extremal problems, and constructive methods are considered. As a new field the theory of circle packings which goes back to P. Koebe is included. The Handbook should be useful for experts as well as for mathematicians working in other areas, as well as for physicists and engineers. · A collection of independent survey articles in the field of GeometricFunction Theory · Existence theorems and qualitative properties of conformal and quasiconformal mappings · A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane)
Geometric Function Theory and Non-linear Analysis
Author: Tadeusz Iwaniec
Publisher: Clarendon Press
ISBN: 9780198509295
Category : Language Arts & Disciplines
Languages : en
Pages : 576
Book Description
Iwaniec (math, Syracuse U.) and Martin (math, U. of Auckland) explain recent developments in the geometry of mappings, related to functions or deformations between subsets of the Euclidean n-space Rn and more generally between manifolds or other geometric objects. Material on mappings intersects with aspects of differential geometry, topology, partial differential equations, harmonic analysis, and the calculus of variations. Chapters cover topics such as conformal mappings, stability of the Mobius group, Sobolev theory and function spaces, the Liouville theorem, even dimensions, Picard and Montel theorems in space, uniformly quasiregular mappings, and quasiconformal groups. c. Book News Inc.
Publisher: Clarendon Press
ISBN: 9780198509295
Category : Language Arts & Disciplines
Languages : en
Pages : 576
Book Description
Iwaniec (math, Syracuse U.) and Martin (math, U. of Auckland) explain recent developments in the geometry of mappings, related to functions or deformations between subsets of the Euclidean n-space Rn and more generally between manifolds or other geometric objects. Material on mappings intersects with aspects of differential geometry, topology, partial differential equations, harmonic analysis, and the calculus of variations. Chapters cover topics such as conformal mappings, stability of the Mobius group, Sobolev theory and function spaces, the Liouville theorem, even dimensions, Picard and Montel theorems in space, uniformly quasiregular mappings, and quasiconformal groups. c. Book News Inc.
Geometric Function Theory in One and Higher Dimensions
Author: Ian Graham
Publisher: CRC Press
ISBN: 9780203911624
Category : Mathematics
Languages : en
Pages : 572
Book Description
This reference details valuable results that lead to improvements in existence theorems for the Loewner differential equation in higher dimensions, discusses the compactness of the analog of the Caratheodory class in several variables, and studies various classes of univalent mappings according to their geometrical definitions. It introduces the in
Publisher: CRC Press
ISBN: 9780203911624
Category : Mathematics
Languages : en
Pages : 572
Book Description
This reference details valuable results that lead to improvements in existence theorems for the Loewner differential equation in higher dimensions, discusses the compactness of the analog of the Caratheodory class in several variables, and studies various classes of univalent mappings according to their geometrical definitions. It introduces the in
Conformal Invariants
Author: Lars V. Ahlfors
Publisher: American Mathematical Soc.
ISBN: 0821869566
Category :
Languages : en
Pages : 177
Book Description
Publisher: American Mathematical Soc.
ISBN: 0821869566
Category :
Languages : en
Pages : 177
Book Description
Semigroups in Geometrical Function Theory
Author: D. Shoikhet
Publisher: Springer Science & Business Media
ISBN: 9401596328
Category : Mathematics
Languages : en
Pages : 231
Book Description
Historically, complex analysis and geometrical function theory have been inten sively developed from the beginning of the twentieth century. They provide the foundations for broad areas of mathematics. In the last fifty years the theory of holomorphic mappings on complex spaces has been studied by many mathemati cians with many applications to nonlinear analysis, functional analysis, differential equations, classical and quantum mechanics. The laws of dynamics are usually presented as equations of motion which are written in the abstract form of a dy namical system: dx / dt + f ( x) = 0, where x is a variable describing the state of the system under study, and f is a vector function of x. The study of such systems when f is a monotone or an accretive (generally nonlinear) operator on the under lying space has been recently the subject of much research by analysts working on quite a variety of interesting topics, including boundary value problems, integral equations and evolution problems (see, for example, [19, 13] and [29]). In a parallel development (and even earlier) the generation theory of one parameter semigroups of holomorphic mappings in en has been the topic of interest in the theory of Markov stochastic processes and, in particular, in the theory of branching processes (see, for example, [63, 127, 48] and [69]).
Publisher: Springer Science & Business Media
ISBN: 9401596328
Category : Mathematics
Languages : en
Pages : 231
Book Description
Historically, complex analysis and geometrical function theory have been inten sively developed from the beginning of the twentieth century. They provide the foundations for broad areas of mathematics. In the last fifty years the theory of holomorphic mappings on complex spaces has been studied by many mathemati cians with many applications to nonlinear analysis, functional analysis, differential equations, classical and quantum mechanics. The laws of dynamics are usually presented as equations of motion which are written in the abstract form of a dy namical system: dx / dt + f ( x) = 0, where x is a variable describing the state of the system under study, and f is a vector function of x. The study of such systems when f is a monotone or an accretive (generally nonlinear) operator on the under lying space has been recently the subject of much research by analysts working on quite a variety of interesting topics, including boundary value problems, integral equations and evolution problems (see, for example, [19, 13] and [29]). In a parallel development (and even earlier) the generation theory of one parameter semigroups of holomorphic mappings in en has been the topic of interest in the theory of Markov stochastic processes and, in particular, in the theory of branching processes (see, for example, [63, 127, 48] and [69]).
Condenser Capacities and Symmetrization in Geometric Function Theory
Author: Vladimir N. Dubinin
Publisher: Springer
ISBN: 3034808437
Category : Science
Languages : en
Pages : 344
Book Description
This is the first systematic presentation of the capacitory approach and symmetrization in the context of complex analysis. The content of the book is original – the main part has not been covered by existing textbooks and monographs. After an introduction to the theory of condenser capacities in the plane, the monotonicity of the capacity under various special transformations (polarization, Gonchar transformation, averaging transformations and others) is established, followed by various types of symmetrization which are one of the main objects of the book. By using symmetrization principles, some metric properties of compact sets are obtained and some extremal decomposition problems are solved. Moreover, the classical and present facts for univalent and multivalent meromorphic functions are proven. This book will be a valuable source for current and future researchers in various branches of complex analysis and potential theory.
Publisher: Springer
ISBN: 3034808437
Category : Science
Languages : en
Pages : 344
Book Description
This is the first systematic presentation of the capacitory approach and symmetrization in the context of complex analysis. The content of the book is original – the main part has not been covered by existing textbooks and monographs. After an introduction to the theory of condenser capacities in the plane, the monotonicity of the capacity under various special transformations (polarization, Gonchar transformation, averaging transformations and others) is established, followed by various types of symmetrization which are one of the main objects of the book. By using symmetrization principles, some metric properties of compact sets are obtained and some extremal decomposition problems are solved. Moreover, the classical and present facts for univalent and multivalent meromorphic functions are proven. This book will be a valuable source for current and future researchers in various branches of complex analysis and potential theory.
Geometric Theory of Generalized Functions with Applications to General Relativity
Author: Michael Grosser
Publisher: Springer Science & Business Media
ISBN: 9781402001451
Category : Mathematics
Languages : en
Pages : 556
Book Description
This work provides the first comprehensive introduction to the nonlinear theory of generalized functions (in the sense of Colombeau's construction) on differentiable manifolds. Particular emphasis is laid on a diffeomorphism invariant geometric approach to embedding the space of Schwartz distributions into algebras of generalized functions. The foundations of a `nonlinear distributional geometry' are developed, supplying a solid base for an increasing number of applications of algebras of generalized functions to questions of a primarily geometric mature, in particular in mathematical physics. Applications of the resulting theory to symmetry group analysis of differential equations and the theory of general relativity are presented in separate chapters. These features distinguish the present volume from earlier introductory texts and monographs on the subject. Audience: The book will be of interest to graduate students as well as to researchers in functional analysis, partial differential equations, differential geometry, and mathematical physics.
Publisher: Springer Science & Business Media
ISBN: 9781402001451
Category : Mathematics
Languages : en
Pages : 556
Book Description
This work provides the first comprehensive introduction to the nonlinear theory of generalized functions (in the sense of Colombeau's construction) on differentiable manifolds. Particular emphasis is laid on a diffeomorphism invariant geometric approach to embedding the space of Schwartz distributions into algebras of generalized functions. The foundations of a `nonlinear distributional geometry' are developed, supplying a solid base for an increasing number of applications of algebras of generalized functions to questions of a primarily geometric mature, in particular in mathematical physics. Applications of the resulting theory to symmetry group analysis of differential equations and the theory of general relativity are presented in separate chapters. These features distinguish the present volume from earlier introductory texts and monographs on the subject. Audience: The book will be of interest to graduate students as well as to researchers in functional analysis, partial differential equations, differential geometry, and mathematical physics.