Holomorphic Spaces

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Holomorphic Functions In The Plane And N Dimensional Space

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Author : Klaus Gürlebeck
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-16

Holomorphic Functions In The Plane And N Dimensional Space written by Klaus Gürlebeck and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-16 with Mathematics categories.

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.

Hyperbolic Complex Spaces

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Author : Shoshichi Kobayashi
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-05-06

Hyperbolic Complex Spaces written by Shoshichi Kobayashi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-05-06 with Mathematics categories.

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.

Quaternionic Hilbert Spaces And Slice Hyperholomorphic Functions

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Author : Daniel Alpay
language : en
Publisher: Springer Nature
Release Date : 2024-12-09

Quaternionic Hilbert Spaces And Slice Hyperholomorphic Functions written by Daniel Alpay and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-09 with Mathematics categories.

The purpose of the present book is to develop the counterparts of Banach and Hilbert spaces in the setting of slice hyperholomorphic functions. Banach and Hilbert spaces of analytic functions, in one or several complex variables, play an important role in analysis and related fields. Besides their intrinsic interest, such spaces have numerous applications. The book is divided into three parts. In the first part, some foundational material on quaternionic functions and functional analysis are introduced. The second part is the core of the book and contains various types of functions spaces ranging from the Hardy spaces, also in the fractional case, to the Fock space extended to the case of quaternions. The third and final part present some further generalization. Researchers in functional analysis and hypercomplex analysis will find this book a key contribution to their field, but also researchers in mathematical physics, especially in quantum mechanics, will benefit from the insights presented.

Complex Analysis And Spectral Theory

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Author : V. P. Havin
language : en
Publisher: Springer
Release Date : 2006-12-08

Complex Analysis And Spectral Theory written by V. P. Havin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.

The Dirichlet Space And Related Function Spaces

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Author : Nicola Arcozzi
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-03

The Dirichlet Space And Related Function Spaces written by Nicola Arcozzi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-03 with Mathematics categories.

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.

Complex Analysis On Infinite Dimensional Spaces

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Author : Sean Dineen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Complex Analysis On Infinite Dimensional Spaces written by Sean Dineen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Infinite dimensional holomorphy is the study of holomorphic or analytic func tions over complex topological vector spaces. The terms in this description are easily stated and explained and allow the subject to project itself ini tially, and innocently, as a compact theory with well defined boundaries. However, a comprehensive study would include delving into, and interacting with, not only the obvious topics of topology, several complex variables theory and functional analysis but also, differential geometry, Jordan algebras, Lie groups, operator theory, logic, differential equations and fixed point theory. This diversity leads to a dynamic synthesis of ideas and to an appreciation of a remarkable feature of mathematics - its unity. Unity requires synthesis while synthesis leads to unity. It is necessary to stand back every so often, to take an overall look at one's subject and ask "How has it developed over the last ten, twenty, fifty years? Where is it going? What am I doing?" I was asking these questions during the spring of 1993 as I prepared a short course to be given at Universidade Federal do Rio de Janeiro during the following July. The abundance of suit able material made the selection of topics difficult. For some time I hesitated between two very different aspects of infinite dimensional holomorphy, the geometric-algebraic theory associated with bounded symmetric domains and Jordan triple systems and the topological theory which forms the subject of the present book.

Dirichlet Series And Holomorphic Functions In High Dimensions

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Author : Andreas Defant
language : en
Publisher: Cambridge University Press
Release Date : 2019-08-08

Dirichlet Series And Holomorphic Functions In High Dimensions written by Andreas Defant and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-08 with Mathematics categories.

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

Geometry And Dynamics Of Groups And Spaces

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Author : Mikhail Kapranov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-05

Geometry And Dynamics Of Groups And Spaces written by Mikhail Kapranov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-05 with Mathematics categories.

Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.

Harmonic Analysis On Commutative Spaces

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Author : Joseph Albert Wolf
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Harmonic Analysis On Commutative Spaces written by Joseph Albert Wolf and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

This study starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces.

Complex Analysis In Locally Convex Spaces

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Author : S. Dineen
language : en
Publisher: Elsevier
Release Date : 2011-08-18

Complex Analysis In Locally Convex Spaces written by S. Dineen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.

Complex Analysis in Locally Convex Spaces