Separately Analytic Functions
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Separately Analytic Functions
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Author : Marek Jarnicki
language : en
Publisher:
Release Date : 2011
Separately Analytic Functions written by Marek Jarnicki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Holomorphic functions categories.
The story of separately holomorphic functions began about 100 years ago. During the second half of the 19th century, it became known that a separately continuous function is not necessarily continuous as a function of all variables. At the beginning of the 20th century, the study of separately holomorphic functions started due to the fundamental work of Osgood and Hartogs. This book provides the first self-contained and complete presentation of the study of separately holomorphic functions, starting from its birth up to current research. Most of the results presented have never been published before in book form. The text is divided into two parts. A more elementary one deals with separately holomorphic functions "without singularities", another addresses the situation of existing singularities. A discussion of the classical results related to separately holomorphic functions leads to the most fundamental result, the classical cross theorem as well as various extensions and generalizations to more complicated "crosses". Additionally, several applications for other classes of "separately regular" functions are given. A solid background in basic complex analysis is a prerequisite. In order to make the book self-contained, all the results needed for its understanding are collected in special introductory chapters and referred to at the beginning of each section. The book is addressed to students and researchers in several complex variables as well as to mathematicians and theoretical physicists who are interested in this area of mathematics.
A Primer Of Real Analytic Functions
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Author : KRANTZ
language : en
Publisher: Birkhäuser
Release Date : 2013-03-09
A Primer Of Real Analytic Functions written by KRANTZ and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Social Science categories.
The subject of real analytic functions is one of the oldest in mathe matical analysis. Today it is encountered early in ones mathematical training: the first taste usually comes in calculus. While most work ing mathematicians use real analytic functions from time to time in their work, the vast lore of real analytic functions remains obscure and buried in the literature. It is remarkable that the most accessible treatment of Puiseux's theorem is in Lefschetz's quite old Algebraic Geometry, that the clearest discussion of resolution of singularities for real analytic manifolds is in a book review by Michael Atiyah, that there is no comprehensive discussion in print of the embedding prob lem for real analytic manifolds. We have had occasion in our collaborative research to become ac quainted with both the history and the scope of the theory of real analytic functions. It seems both appropriate and timely for us to gather together this information in a single volume. The material presented here is of three kinds. The elementary topics, covered in Chapter 1, are presented in great detail. Even results like a real ana lytic inverse function theorem are difficult to find in the literature, and we take pains here to present such topics carefully. Topics of middling difficulty, such as separate real analyticity, Puiseux series, the FBI transform, and related ideas (Chapters 2-4), are covered thoroughly but rather more briskly.
Complex Analysis
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Author : Klas Diederich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Complex Analysis written by Klas Diederich 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 2013-04-17 with Technology & Engineering categories.
This volume contains the Proceedings of the International Workshop "Complex Analysis", which was held from February 12-16, 1990, in Wuppertal (Germany) in honour of H. Grauert, one of the most creative mathematicians in Complex Analysis of this century. In complete accordance with the width of the work of Grauert the book contains research notes and longer articles of many important mathematicians from all areas of Complex Analysis (Altogether there a re 49 articles in the volume). Some of the main subjects are: Cau chy-Riemann Equations with estimates, q-convexity, CR structures, deformation theory, envelopes of holomorphy, function algebras, complex group actions, Hodge theory, instantons, Kähler geometry, Lefschetz theorems, holomorphic mappings, Nevanlinna theory, com plex singularities, twistor theory, uniformization.
Analytic Functions Of Several Complex Variables
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Author : Robert C. Gunning
language : en
Publisher: American Mathematical Society
Release Date : 2022-08-25
Analytic Functions Of Several Complex Variables written by Robert C. Gunning and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-25 with Mathematics categories.
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.
Analysis Meets Geometry
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Author : Mats Andersson
language : en
Publisher: Birkhäuser
Release Date : 2017-09-04
Analysis Meets Geometry written by Mats Andersson and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-04 with Mathematics categories.
This book is dedicated to the memory of Mikael Passare, an outstanding Swedish mathematician who devoted his life to developing the theory of analytic functions in several complex variables and exploring geometric ideas first-hand. It includes several papers describing Mikael’s life as well as his contributions to mathematics, written by friends of Mikael’s who share his attitude and passion for science. A major section of the book presents original research articles that further develop Mikael’s ideas and which were written by his former students and co-authors. All these mathematicians work at the interface of analysis and geometry, and Mikael’s impact on their research cannot be underestimated. Most of the contributors were invited speakers at the conference organized at Stockholm University in his honor. This book is an attempt to express our gratitude towards this great mathematician, who left us full of energy and new creative mathematical ideas.
Functional Analysis And Complex Analysis
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Author : Aydin Aytuna
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-03-20
Functional Analysis And Complex Analysis written by Aydin Aytuna 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 2009-03-20 with Mathematics categories.
In recent years, the interplay between the methods of functional analysis and complex analysis has led to some remarkable results in a wide variety of topics. It turned out that the structure of spaces of holomorphic functions is fundamentally linked to certain invariants initially defined on abstract Frechet spaces as well as to the developments in pluripotential theory. The aim of this volume is to document some of the original contributions to this topic presented at a conference held at Sabanci University in Istanbul, in September 2007. This volume also contains some surveys that give an overview of the state of the art and initiate further research in the interplay between functional and complex analysis.
Several Complex Variables And Complex Geometry Part I
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Author : Eric Bedford
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Several Complex Variables And Complex Geometry Part I written by Eric Bedford 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 1991 with Mathematics categories.
Modern Analysis Of Automorphic Forms By Example
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Author : Paul Garrett
language : en
Publisher: Cambridge University Press
Release Date : 2018-09-20
Modern Analysis Of Automorphic Forms By Example written by Paul Garrett 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 2018-09-20 with Mathematics categories.
Volume 2 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.
Distributive Lattices And Their Applications In Complex Analysis
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Author : Viktor Viktorovich Zharinov
language : en
Publisher: American Mathematical Soc.
Release Date : 1985
Distributive Lattices And Their Applications In Complex Analysis written by Viktor Viktorovich Zharinov 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 1985 with Mathematics categories.
Algebraic methods have penetrated deeply into contemporary complex analysis, having an essential influence on both the choice of problems and on the methods for solving them. This monograph deals with the applications of distributive lattices of subspaces to problems in multidimensional complex analysis.
Holding And Psychoanalysis
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Author : Joyce Anne Slochower
language : en
Publisher: Routledge
Release Date : 2013-04-15
Holding And Psychoanalysis written by Joyce Anne Slochower and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-15 with Psychology categories.
In Holding and Psychoanalysis: A Relational Perspective, Joyce Slochower brings a contemporary relational framework to bear on Winnicott's notion of the analytic holding environment. She presents a fresh, thought-provoking, and clinically useful integration of Winnicott's seminal insights with contemporary relational and feminist/psychoanalytic contributions. Seeking to broaden the concept of holding beyond work with severely regressed patients, she addresses holding in a variety of clinical contexts and focuses especially on holding processes in relation to issues of dependence, self-involvement, and hate. She also considers clinical work with patients "on the edge" - patients who seem deperately to need a holding experience that remains paradoxically elusive. Slochower begins her study by questioning the therapeutic limitations of an interactive style. There are times, she proposes, when certain patients simply cannot tolerate evidence of the analyst's separate subjective presence and instead need a holding experience. Though this holding function is essential to work with difficult patients, it enters into the treatment of all patients, whether as figure or ground. Slochower's relational understanding of holding leads her to consider the impact of holding on patient and analyst alike. Throughout, she emphasizes the analyst's and the patient's co-construction, during moments of holding, of an essential illusion of analytic attunement; this illusion serves to protect the patient from potentially disruptive aspects of the analyst's subjective presence. Slochower's case vignettes helpfully illuminate the intersubjective aspects of the holding process, including the clinical picture when a holding frame fails. She elaborates her thesis by considering the therapeutic function of holding in mourning. And she concludes her study with a cogent examination of the theoretical and clinical limitations of working with a holding process. A welcome reprise on an essential Winnicottian theme, Holding and Psychoanalysis broadens and deepens our understanding of the therapeutic role of the analyst's holding function.