Holomorphic Spaces

Holomorphic Spaces
Author :
Publisher : Cambridge University Press
Total Pages : 490
Release :
ISBN-10 : 0521631939
ISBN-13 : 9780521631938
Rating : 4/5 (39 Downloads)

Synopsis Holomorphic Spaces by : Sheldon Jay Axler

Expository articles describing the role Hardy spaces, Bergman spaces, Dirichlet spaces, and Hankel and Toeplitz operators play in modern analysis.

Spaces of Holomorphic Functions in the Unit Ball

Spaces of Holomorphic Functions in the Unit Ball
Author :
Publisher : Springer Science & Business Media
Total Pages : 281
Release :
ISBN-10 : 9780387275390
ISBN-13 : 0387275398
Rating : 4/5 (90 Downloads)

Synopsis Spaces of Holomorphic Functions in the Unit Ball by : Kehe Zhu

Can be used as a graduate text Contains many exercises Contains new results

Holomorphic Functions in the Plane and n-dimensional Space

Holomorphic Functions in the Plane and n-dimensional Space
Author :
Publisher : Springer Science & Business Media
Total Pages : 407
Release :
ISBN-10 : 9783764382711
ISBN-13 : 3764382716
Rating : 4/5 (11 Downloads)

Synopsis Holomorphic Functions in the Plane and n-dimensional Space by : Klaus Gürlebeck

Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30 years the so-called quaternionic and Clifford or hypercomplex analysis successfully developed to a powerful theory with many applications in analysis, engineering and mathematical physics. This textbook introduces both to classical and higher-dimensional results based on a uniform notion of holomorphy. Historical remarks, lots of examples, figures and exercises accompany each chapter.

Introduction to the Theory of Analytic Spaces

Introduction to the Theory of Analytic Spaces
Author :
Publisher : Springer
Total Pages : 149
Release :
ISBN-10 : 9783540348450
ISBN-13 : 354034845X
Rating : 4/5 (50 Downloads)

Synopsis Introduction to the Theory of Analytic Spaces by : Raghavan Narasimhan

Holomorphic Automorphism Groups in Banach Spaces

Holomorphic Automorphism Groups in Banach Spaces
Author :
Publisher : Elsevier
Total Pages : 305
Release :
ISBN-10 : 9780080872162
ISBN-13 : 0080872166
Rating : 4/5 (62 Downloads)

Synopsis Holomorphic Automorphism Groups in Banach Spaces by : J.M. Isidro

Holomorphic Automorphism Groups in Banach Spaces

Dirichlet Series and Holomorphic Functions in High Dimensions

Dirichlet Series and Holomorphic Functions in High Dimensions
Author :
Publisher : Cambridge University Press
Total Pages : 709
Release :
ISBN-10 : 9781108476713
ISBN-13 : 1108476716
Rating : 4/5 (13 Downloads)

Synopsis Dirichlet Series and Holomorphic Functions in High Dimensions by : Andreas Defant

Using contemporary concepts, this book describes the interaction between Dirichlet series and holomorphic functions in high dimensions.

Hyperbolic Complex Spaces

Hyperbolic Complex Spaces
Author :
Publisher : Springer Science & Business Media
Total Pages : 480
Release :
ISBN-10 : 9783662035825
ISBN-13 : 3662035820
Rating : 4/5 (25 Downloads)

Synopsis Hyperbolic Complex Spaces by : Shoshichi Kobayashi

In the three decades since the introduction of the Kobayashi distance, the subject of hyperbolic complex spaces and holomorphic mappings has grown to be a big industry. This book gives a comprehensive and systematic account on the Carathéodory and Kobayashi distances, hyperbolic complex spaces and holomorphic mappings with geometric methods. A very complete list of references should be useful for prospective researchers in this area.

Stein Manifolds and Holomorphic Mappings

Stein Manifolds and Holomorphic Mappings
Author :
Publisher : Springer
Total Pages : 569
Release :
ISBN-10 : 9783319610580
ISBN-13 : 3319610589
Rating : 4/5 (80 Downloads)

Synopsis Stein Manifolds and Holomorphic Mappings by : Franc Forstnerič

This book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Stein manifolds. Oka theory is the field of complex analysis dealing with global problems on Stein manifolds which admit analytic solutions in the absence of topological obstructions. The exposition in the present volume focuses on the notion of an Oka manifold introduced by the author in 2009. It explores connections with elliptic complex geometry initiated by Gromov in 1989, with the Andersén-Lempert theory of holomorphic automorphisms of complex Euclidean spaces and of Stein manifolds with the density property, and with topological methods such as homotopy theory and the Seiberg-Witten theory. Researchers and graduate students interested in the homotopy principle in complex analysis will find this book particularly useful. It is currently the only work that offers a comprehensive introduction to both the Oka theory and the theory of holomorphic automorphisms of complex Euclidean spaces and of other complex manifolds with large automorphism groups.

Introduction to Complex Analytic Geometry

Introduction to Complex Analytic Geometry
Author :
Publisher : Birkhäuser
Total Pages : 535
Release :
ISBN-10 : 9783034876179
ISBN-13 : 3034876173
Rating : 4/5 (79 Downloads)

Synopsis Introduction to Complex Analytic Geometry by : Stanislaw Lojasiewicz

facts. An elementary acquaintance with topology, algebra, and analysis (in cluding the notion of a manifold) is sufficient as far as the understanding of this book is concerned. All the necessary properties and theorems have been gathered in the preliminary chapters -either with proofs or with references to standard and elementary textbooks. The first chapter of the book is devoted to a study of the rings Oa of holomorphic functions. The notions of analytic sets and germs are introduced in the second chapter. Its aim is to present elementary properties of these objects, also in connection with ideals of the rings Oa. The case of principal germs (§5) and one-dimensional germs (Puiseux theorem, §6) are treated separately. The main step towards understanding of the local structure of analytic sets is Ruckert's descriptive lemma proved in Chapter III. Among its conse quences is the important Hilbert Nullstellensatz (§4). In the fourth chapter, a study of local structure (normal triples, § 1) is followed by an exposition of the basic properties of analytic sets. The latter includes theorems on the set of singular points, irreducibility, and decom position into irreducible branches (§2). The role played by the ring 0 A of an analytic germ is shown (§4). Then, the Remmert-Stein theorem on re movable singularities is proved (§6). The last part of the chapter deals with analytically constructible sets (§7).

Analytic Functions of Several Complex Variables

Analytic Functions of Several Complex Variables
Author :
Publisher : American Mathematical Society
Total Pages : 334
Release :
ISBN-10 : 9781470470661
ISBN-13 : 1470470667
Rating : 4/5 (61 Downloads)

Synopsis Analytic Functions of Several Complex Variables by : Robert C. Gunning

The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. After initial successes by Poincaré and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable. Beginning in the 1930s, initially through the work of Oka, then H. Cartan, and continuing with the work of Grauert, Remmert, and others, new tools were introduced into the theory of several complex variables that resolved many of the open problems and fundamentally changed the landscape of the subject. These tools included a central role for sheaf theory and increased uses of topology and algebra. The book by Gunning and Rossi was the first of the modern era of the theory of several complex variables, which is distinguished by the use of these methods. The intention of Gunning and Rossi's book is to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces. Fundamental concepts and techniques are discussed as early as possible. The first chapter covers material suitable for a one-semester graduate course, presenting many of the central problems and techniques, often in special cases. The later chapters give more detailed expositions of sheaf theory for analytic functions and the theory of complex analytic spaces. Since its original publication, this book has become a classic resource for the modern approach to functions of several complex variables and the theory of analytic spaces. Further information about this book, including updates, can be found at the following URL: www.ams.org/publications/authors/books/postpub/chel-368.