Distribution Of Values Of Holomorphic Mappings

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Distribution Of Values Of Holomorphic Mappings

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Author : Boris Vladimirovich Shabat
language : en
Publisher: American Mathematical Soc.
Release Date : 1985-12-31

Distribution Of Values Of Holomorphic Mappings written by Boris Vladimirovich Shabat 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 1985-12-31 with Mathematics categories.

A vast literature has grown up around the value distribution theory of meromorphic functions, synthesized by Rolf Nevanlinna in the 1920s and singled out by Hermann Weyl as one of the greatest mathematical achievements of this century. The multidimensional aspect, involving the distribution of inverse images of analytic sets under holomorphic mappings of complex manifolds, has not been fully treated in the literature. This volume thus provides a valuable introduction to multivariate value distribution theory and a survey of some of its results, rich in relations to both algebraic and differential geometry and surely one of the most important branches of the modern geometric theory of functions of a complex variable. Since the book begins with preparatory material from the contemporary geometric theory of functions, only a familiarity with the elements of multidimensional complex analysis is necessary background to understand the topic. After proving the two main theorems of value distribution theory, the author goes on to investigate further the theory of holomorphic curves and to provide generalizations and applications of the main theorems, focusing chiefly on the work of Soviet mathematicians.

Value Distribution Theory

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Author : I. Laine
language : en
Publisher: Springer
Release Date : 2006-11-15

Value Distribution Theory written by I. Laine and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Arithmetic Of Probability Distributions And Characterization Problems On Abelian Groups

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Author : Gennadij M. Fel'dman
language : en
Publisher: American Mathematical Soc.
Release Date :

Arithmetic Of Probability Distributions And Characterization Problems On Abelian Groups written by Gennadij M. Fel'dman 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 with Mathematics categories.

This book studies the problem of the decomposition of a given random variable introduction a sum of independent random variables (components). The central feature of the book is Feldman's use of powerful analytical techniques.

Hyperbolic Complex Spaces

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Author : Shoshichi Kobayashi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

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 2013-03-09 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.

Theory Of Entire And Meromorphic Functions

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Author : Guan-hou Zhang
language : en
Publisher: American Mathematical Soc.
Release Date : 1993-01-01

Theory Of Entire And Meromorphic Functions written by Guan-hou Zhang 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 1993-01-01 with Mathematics categories.

This book was originally written in Chinese in 1986 by the noted complex analyst Zhang Guan-Hou, who was a research fellow at the Academia Sinica. The book provides a basic introduction to the development of the theory of entire and meromorphic functions from the 1950s to the early 1980s. After an opening chapter introducing fundamentals of Nevanlinna's value distribution theory, this book discusses various relationships among and developments of three central concepts: deficient value, asymptotic value, and singular direction. This book describes many significant results and research directions developed by Zhang and other Chinese complex analysts and published in Chinese mathematical journals. A comprehensive and self-contained reference, this book is useful for graduate students and researchers in complex analysis.

Arithmetic Of Probability Distributions And Characterization Problems On Abelian Groups

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Author : Gennadiĭ Mikhaĭlovich Felʹdman
language : en
Publisher: American Mathematical Soc.
Release Date : 1993

Arithmetic Of Probability Distributions And Characterization Problems On Abelian Groups written by Gennadiĭ Mikhaĭlovich Felʹdman 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 1993 with Mathematics categories.

This book studies the problem of the decomposition of a given random variable into a sum of independent random variables (components). Starting from the famous Cramer theorem, which says that all components of a normal random variable are also normal random variables, the central feature of the book is Feldman's use of powerful analytical techniques. In the algebraic case, one cannot directly use analytic methods because of the absence of a natural analytic structure on the dual group, which is the domain of characteristic functions. Nevertheless, the methods developed in this book allow one to apply analytic techniques in the algebraic setting. The first part of the book presents results on the arithmetic of probability distributions of random variables with values in a locally compact abelian group. The second part studies problems of characterization of a Gaussian distribution of a locally compact abelian group by the independence or identical distribution of its linear statistics.

Unicity Of Meromorphic Mappings

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Author : Pei-Chu Hu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18

Unicity Of Meromorphic Mappings written by Pei-Chu Hu 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 2013-04-18 with Mathematics categories.

For a given meromorphic function I(z) and an arbitrary value a, Nevanlinna's value distribution theory, which can be derived from the well known Poisson-Jensen for mula, deals with relationships between the growth of the function and quantitative estimations of the roots of the equation: 1 (z) - a = O. In the 1920s as an application of the celebrated Nevanlinna's value distribution theory of meromorphic functions, R. Nevanlinna [188] himself proved that for two nonconstant meromorphic func tions I, 9 and five distinctive values ai (i = 1,2,3,4,5) in the extended plane, if 1 1- (ai) = g-l(ai) 1M (ignoring multiplicities) for i = 1,2,3,4,5, then 1 = g. Fur 1 thermore, if 1- (ai) = g-l(ai) CM (counting multiplicities) for i = 1,2,3 and 4, then 1 = L(g), where L denotes a suitable Mobius transformation. Then in the 19708, F. Gross and C. C. Yang started to study the similar but more general questions of two functions that share sets of values. For instance, they proved that if 1 and 9 are two nonconstant entire functions and 8 , 82 and 83 are three distinctive finite sets such 1 1 that 1- (8 ) = g-1(8 ) CM for i = 1,2,3, then 1 = g.

Subgroups Of Teichmuller Modular Groups

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Author : Nikolai V. Ivanov
language : en
Publisher: American Mathematical Soc.
Release Date : 1992-12-28

Subgroups Of Teichmuller Modular Groups written by Nikolai V. Ivanov 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 1992-12-28 with Mathematics categories.

Teichmuller modular groups, also known as mapping class groups of surfaces, serve as a meeting ground for several branches of mathematics, including low-dimensional topology, the theory of Teichmuller spaces, group theory, and, more recently, mathematical physics. The present work focuses mainly on the group-theoretic properties of these groups and their subgroups. The technical tools come from Thurston's theory of surfaces - his classification of surface diffeomorphisms and the theory of measured foliations on surfaces.The guiding principle of this investigation is a deep analogy between modular groups and linear groups. For some of the central results of the theory of linear groups (such as the theorems of Platonov, Tits, and Margulis-Soifer), the author provides analogous results for the case of subgroups of modular groups. The results also include a clear geometric picture of subgroups of modular groups and their action on Thurston's boundary of Teichmuller spaces. Aimed at research mathematicians and graduate students, this book is suitable as supplementary material in advanced graduate courses.

Typical Singularities Of Differential 1 Forms And Pfaffian Equations

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Author : Mikhail Zhitomirskiĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 1992

Typical Singularities Of Differential 1 Forms And Pfaffian Equations written by Mikhail Zhitomirskiĭ 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 1992 with Mathematics categories.

Singularities and the classification of 1-forms and Pfaffian equations are interesting not only as classical problems, but also because of their applications in contact geometry, partial differential equations, control theory, nonholonomic dynamics, and variational problems. In addition to collecting results on the geometry of singularities and classification of differential forms and Pfaffian equations, this monograph discusses applications and closely related classification problems. Zhitomirskii presents proofs with all results and ends each chapter with a summary of the main results, a tabulation of the singularities, and a list of the normal forms. The main results of the book are also collected together in the introduction.

Carleman S Formulas In Complex Analysis

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Author : L.A. Aizenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Carleman S Formulas In Complex Analysis written by L.A. Aizenberg 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.

Integral representations of holomorphic functions play an important part in the classical theory of functions of one complex variable and in multidimensional com plex analysis (in the later case, alongside with integration over the whole boundary aD of a domain D we frequently encounter integration over the Shilov boundary 5 = S(D)). They solve the classical problem of recovering at the points of a do main D a holomorphic function that is sufficiently well-behaved when approaching the boundary aD, from its values on aD or on S. Alongside with this classical problem, it is possible and natural to consider the following one: to recover the holomorphic function in D from its values on some set MeaD not containing S. Of course, M is to be a set of uniqueness for the class of holomorphic functions under consideration (for example, for the functions continuous in D or belonging to the Hardy class HP(D), p ~ 1).