Spaces Of Holomorphic Functions In The Unit Ball PDF Download
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Author | : Kehe Zhu |
Publisher | : Springer Science & Business Media |
Total Pages | : 281 |
Release | : 2006-03-22 |
Genre | : Mathematics |
ISBN | : 0387275398 |
Download Spaces of Holomorphic Functions in the Unit Ball Book in PDF, ePub and Kindle
Can be used as a graduate text Contains many exercises Contains new results
Author | : Kehe Zhu |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2008-11-01 |
Genre | : Mathematics |
ISBN | : 9780387501390 |
Download Spaces of Holomorphic Functions in the Unit Ball Book in PDF, ePub and Kindle
Can be used as a graduate text Contains many exercises Contains new results
Author | : Thomas J. Watson IBM Research Center |
Publisher | : |
Total Pages | : 12 |
Release | : 1986 |
Genre | : |
ISBN | : |
Download N-width for Holomorphic Functions on the Unit Ball in N-space Book in PDF, ePub and Kindle
Author | : Walter Rudin |
Publisher | : American Mathematical Soc. |
Total Pages | : 100 |
Release | : 1986 |
Genre | : Mathematics |
ISBN | : 9780821889084 |
Download New Constructions of Functions Holomorphic in the Unit Ball of CN Book in PDF, ePub and Kindle
Author | : W. Rudin |
Publisher | : Springer Science & Business Media |
Total Pages | : 449 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461380987 |
Download Function Theory in the Unit Ball of Cn Book in PDF, ePub and Kindle
Around 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 | : Hakan Hedenmalm |
Publisher | : Springer Science & Business Media |
Total Pages | : 299 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461204976 |
Download Theory of Bergman Spaces Book in PDF, ePub and Kindle
Fifteen years ago, most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unlikely, yet today the situation has completely changed. For several years, research interest and activity have expanded in this area and there are now rich theories describing the Bergman spaces and their operators. This book is a timely treatment of the theory, written by three of the major players in the field.
Author | : |
Publisher | : |
Total Pages | : 10 |
Release | : 1983 |
Genre | : |
ISBN | : |
Download On the Approximation of Holomorphic Functions in the Unit Ball of C Book in PDF, ePub and Kindle
Author | : Frank Beatrous |
Publisher | : |
Total Pages | : 68 |
Release | : 1989 |
Genre | : Holomorphic functions |
ISBN | : |
Download Holomorphic Sobolev Spaces on the Ball Book in PDF, ePub and Kindle
Author | : Paula A. Russo |
Publisher | : |
Total Pages | : 170 |
Release | : 1984 |
Genre | : Holomorphic functions |
ISBN | : |
Download Boundary Behavior of Holomorphic Functions in the Unit Ball of C[subscript N] Book in PDF, ePub and Kindle
Author | : Nicola Arcozzi |
Publisher | : American Mathematical Soc. |
Total Pages | : 536 |
Release | : 2019-09-03 |
Genre | : Dirichlet principle |
ISBN | : 1470450828 |
Download The Dirichlet Space and Related Function Spaces Book in PDF, ePub and Kindle
The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The theory is related to such important themes as multipliers, reproducing kernels, and Besov spaces, among others. The authors present the theory of the Dirichlet space and related spaces starting with classical results and including some quite recent achievements like Dirichlet-type spaces of functions in several complex variables and the corona problem. The first part of this book is an introduction to the function theory and operator theory of the classical Dirichlet space, a space of holomorphic functions on the unit disk defined by a smoothness criterion. The Dirichlet space is also a Hilbert space with a reproducing kernel, and is the model for the dyadic Dirichlet space, a sequence space defined on the dyadic tree. These various viewpoints are used to study a range of topics including the Pick property, multipliers, Carleson measures, boundary values, zero sets, interpolating sequences, the local Dirichlet integral, shift invariant subspaces, and Hankel forms. Recurring themes include analogies, sometimes weak and sometimes strong, with the classical Hardy space; and the analogy with the dyadic Dirichlet space. The final chapters of the book focus on Besov spaces of holomorphic functions on the complex unit ball, a class of Banach spaces generalizing the Dirichlet space. Additional techniques are developed to work with the nonisotropic complex geometry, including a useful invariant definition of local oscillation and a sophisticated variation on the dyadic Dirichlet space. Descriptions are obtained of multipliers, Carleson measures, interpolating sequences, and multiplier interpolating sequences; estimates are obtained to prove corona theorems.