Vector Valued Nevanlinna Theory
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Vector Valued Nevanlinna Theory
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Author : Hans J. W. Ziegler
language : en
Publisher: Pitman Publishing
Release Date : 1982
Vector Valued Nevanlinna Theory written by Hans J. W. Ziegler and has been published by Pitman Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
Vector Valued Nevanlinna Theory
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Author : H. J. Ziegler
language : en
Publisher: Halsted Press
Release Date : 1983-12-12
Vector Valued Nevanlinna Theory written by H. J. Ziegler and has been published by Halsted Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-12-12 with categories.
Meromorphic Functions And Linear Algebra
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Author : Olavi Nevanlinna
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Meromorphic Functions And Linear Algebra written by Olavi Nevanlinna 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 2003 with Mathematics categories.
This volume describes for the first time in monograph form important applications in numerical methods of linear algebra. The author presents new material and extended results from recent papers in a very readable style. The main goal of the book is to study the behavior of the resolvent of a matrix under the perturbation by low rank matrices. Whereas the eigenvalues (the poles of the resolvent) and the pseudospectra (the sets where the resolvent takes large values) can move dramatically under such perturbations, the growth of the resolvent as a matrix-valued meromorphic function remains essentially unchanged. This has practical implications to the analysis of iterative solvers for large systems of linear algebraic equations. First, the book introduces the basics of value distribution theory of meromorphic scalar functions. It then introduces a new nonlinear tool for linear algebra, the total logarithmic size of a matrix, which allows for a nontrivial generalization of Rolf Nevanlinna's characteristic function from the scalar theory to matrix- and operator-valued functions. In particular, the theory of perturbations by low rank matrices becomes possible. As an example, if the spectrum of a normal matrix collapses under a low rank perturbation, there is always a compensation in terms of the loss of orthogonality of the eigenvectors. This qualitative phenomenon is made quantitative by using the new tool. Applications are given to rational approximation, to the Kreiss matrix theorem, and to convergence of Krylov solvers. The book is intended for researchers in mathematics in general and especially for those working in numerical linear algebra. Much of the book is understandable if the reader has a good background in linear algebra and a first course in complex analysis.
Value Distribution Theory Related To Number Theory
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Author : Pei-Chu Hu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-10-06
Value Distribution Theory Related To Number Theory 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 2006-10-06 with Mathematics categories.
The subject of the book is Diophantine approximation and Nevanlinna theory. This book proves not just some new results and directions but challenging open problems in Diophantine approximation and Nevanlinna theory. The authors’ newest research activities on these subjects over the past eight years are collected here. Some of the significant findings are the proof of Green-Griffiths conjecture by using meromorphic connections and Jacobian sections, generalized abc-conjecture, and more.
Value Distribution Theory For Meromorphic Maps
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Author : Wilhelm Stoll
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Value Distribution Theory For Meromorphic Maps written by Wilhelm Stoll 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 2013-06-29 with Science categories.
Value distribution theory studies the behavior of mermorphic maps. Let f: M - N be a merom orphic map between complex manifolds. A target family CI ~ (Ea1aEA of analytic subsets Ea of N is given where A is a connected. compact complex manifold. The behavior of the inverse 1 family ["'(CI) = (f- {E )laEA is investigated. A substantial theory has been a created by many contributors. Usually the targets Ea stay fixed. However we can consider a finite set IJ of meromorphic maps g : M - A and study the incidence f{z) E Eg(z) for z E M and some g E IJ. Here we investigate this situation: M is a parabolic manifold of dimension m and N = lP n is the n-dimensional projective space. The family of hyperplanes in lP n is the target family parameterized by the dual projective space lP* We obtain a Nevanlinna theory consisting of several n First Main Theorems. Second Main Theorems and Defect Relations and extend recent work by B. Shiffman and by S. Mori. We use the Ahlfors-Weyl theory modified by the curvature method of Cowen and Griffiths. The Introduction consists of two parts. In Part A. we sketch the theory for fixed targets to provide background for those who are familar with complex analysis but are not acquainted with value distribution theory.
Nevanlinna Theory And Its Relation To Diophantine Approximation
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Author : Min Ru
language : en
Publisher: World Scientific
Release Date : 2001
Nevanlinna Theory And Its Relation To Diophantine Approximation written by Min Ru and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
It was discovered recently that Nevanlinna theory and Diophantine approximation bear striking similarities and connections. This book provides an introduction to both Nevanlinna theory and Diophantine approximation, with emphasis on the analogy between these two subjects. Each chapter is divided into part A and part B. Part A deals with Nevanlinna theory and part B covers Diophantine approximation. At the end of each chapter, a table is provided to indicate the correspondence of theorems. Contents: Nevanlinna Theory for Meromorphic Functions and Roth's Theorem; Holomorphic Curves into Compact Riemann Surfaces and Theorems of Siegel, Roth, and Faltings; Holomorphic Curves in Pn(C) and Schmidt's Sub-Space Theorem; The Moving Target Problems; Equi-Dimensional Nevanlinna Theory and Vojta's Conjecture; Holomorphic Curves in Abelian Varieties and the Theorem of Faltings; Complex Hyperbolic Manifolds and Lang's Conjecture. Readership: Researchers in complex analysis, number theory and complex geometry.
Vector Valued Functions And Their Applications
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Author : Chuang-Gan Hu
language : en
Publisher: Springer
Release Date : 1992-03-31
Vector Valued Functions And Their Applications written by Chuang-Gan Hu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-31 with Mathematics categories.
This book is the first to be devoted to the theory of vector-valued functions with one variable. This theory is one of the fundamental tools employed in modern physics, the spectral theory of operators, approximation of analytic operators, analytic mappings between vectors, and vector-valued functions of several variables. The book contains three chapters devoted to the theory of normal functions, Hp-space, and vector-valued functions and their applications. Among the topics dealt with are the properties of complex functions in a complex plane and infinite-dimensional spaces, and the solution of vector-valued integral equations and boundary value problems by complex analysis and functional analysis, which involve methods which can be applied to problems in operations research and control theory. Much original research is included. This volume will be of interest to those whose work involves complex analysis and control theory, and can be recommended as a graduate text in these areas.
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.
Minimal Surfaces Through Nevanlinna Theory
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Author : Min Ru
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-05-08
Minimal Surfaces Through Nevanlinna Theory written by Min Ru and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-08 with Mathematics categories.
The study of minimal surfaces is an important subject in differential geometry, and Nevanlinna theory is an important subject in complex analysis and complex geometry. This book discusses the interaction between these two subjects. In particular, it describes the study of the value distribution properties of the Gauss map of minimal surfaces through Nevanlinna theory, a project initiated by the prominent differential geometers Shiing-Shen Chern and Robert Osserman.
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.