Function Theory in the Unit Ball of [n-dimensional Complex Space]
Author: Walter Rudin
Publisher:
Published: 1980
Total Pages: 436
ISBN-13:
DOWNLOAD EBOOKRead and Download eBook Full
Author: Walter Rudin
Publisher:
Published: 1980
Total Pages: 436
ISBN-13:
DOWNLOAD EBOOKAuthor: W. Rudin
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 449
ISBN-13: 1461380987
DOWNLOAD EBOOKAround 1970, an abrupt change occurred in the study of holomorphic functions of several complex variables. Sheaves vanished into the back ground, and attention was focused on integral formulas and on the "hard analysis" problems that could be attacked with them: boundary behavior, complex-tangential phenomena, solutions of the J-problem with control over growth and smoothness, quantitative theorems about zero-varieties, and so on. The present book describes some of these developments in the simple setting of the unit ball of en. There are several reasons for choosing the ball for our principal stage. The ball is the prototype of two important classes of regions that have been studied in depth, namely the strictly pseudoconvex domains and the bounded symmetric ones. The presence of the second structure (i.e., the existence of a transitive group of automorphisms) makes it possible to develop the basic machinery with a minimum of fuss and bother. The principal ideas can be presented quite concretely and explicitly in the ball, and one can quickly arrive at specific theorems of obvious interest. Once one has seen these in this simple context, it should be much easier to learn the more complicated machinery (developed largely by Henkin and his co-workers) that extends them to arbitrary strictly pseudoconvex domains. In some parts of the book (for instance, in Chapters 14-16) it would, however, have been unnatural to confine our attention exclusively to the ball, and no significant simplifications would have resulted from such a restriction.
Author: Walter Rudin
Publisher:
Published: 1980
Total Pages: 436
ISBN-13:
DOWNLOAD EBOOKAuthor: Carl H. FitzGerald
Publisher: World Scientific
Published: 2004
Total Pages: 360
ISBN-13: 9789812702500
DOWNLOAD EBOOKThe papers contained in this book address problems in one and several complex variables. The main theme is the extension of geometric function theory methods and theorems to several complex variables. The papers present various results on the growth of mappings in various classes as well as observations about the boundary behavior of mappings, via developing and using some semi group methods.
Author: Ian Graham
Publisher: CRC Press
Published: 2003-03-18
Total Pages: 572
ISBN-13: 9780203911624
DOWNLOAD EBOOKThis 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
Author: Sheng Gong
Publisher: World Scientific
Published: 2004-09-23
Total Pages: 353
ISBN-13: 9814481912
DOWNLOAD EBOOKThe papers contained in this book address problems in one and several complex variables. The main theme is the extension of geometric function theory methods and theorems to several complex variables. The papers present various results on the growth of mappings in various classes as well as observations about the boundary behavior of mappings, via developing and using some semi group methods.
Author: Steven George Krantz
Publisher: American Mathematical Soc.
Published: 2001
Total Pages: 586
ISBN-13: 0821827243
DOWNLOAD EBOOKEmphasizing 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.
Author: Sorin G. Gal
Publisher: Nova Publishers
Published: 2002
Total Pages: 340
ISBN-13: 9781590333648
DOWNLOAD EBOOKIntroduction to Geometric Function Theory of Hypercomplex Variables
Author: Le Hai Khoi
Publisher: Springer Nature
Published: 2023-10-09
Total Pages: 261
ISBN-13: 3031397045
DOWNLOAD EBOOKThis monograph provides a comprehensive study of a typical and novel function space, known as the $\mathcal{N}_p$ spaces. These spaces are Banach and Hilbert spaces of analytic functions on the open unit disk and open unit ball, and the authors also explore composition operators and weighted composition operators on these spaces. The book covers a significant portion of the recent research on these spaces, making it an invaluable resource for those delving into this rapidly developing area. The authors introduce various weighted spaces, including the classical Hardy space $H^2$, Bergman space $B^2$, and Dirichlet space $\mathcal{D}$. By offering generalized definitions for these spaces, readers are equipped to explore further classes of Banach spaces such as Bloch spaces $\mathcal{B}^p$ and Bergman-type spaces $A^p$. Additionally, the authors extend their analysis beyond the open unit disk $\mathbb{D}$ and open unit ball $\mathbb{B}$ by presenting families of entire functions in the complex plane $\mathbb{C}$ and in higher dimensions. The Theory of $\mathcal{N}_p$ Spaces is an ideal resource for researchers and PhD students studying spaces of analytic functions and operators within these spaces.
Author: Sheng Gong
Publisher: World Scientific Publishing Company
Published: 2007-04-26
Total Pages: 258
ISBN-13: 9813106980
DOWNLOAD EBOOKA concise textbook on complex analysis for undergraduate and graduate students, this book is written from the viewpoint of modern mathematics: the Bar {Partial}-equation, differential geometry, Lie groups, all the traditional material on complex analysis is included. Setting it apart from others, the book makes many statements and proofs of classical theorems in complex analysis simpler, shorter and more elegant: for example, the Mittag-Leffer theorem is proved using the Bar {Partial}-equation, and the Picard theorem is proved using the methods of differential geometry.