Meromorphic Functions And Linear Algebra
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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.
Formal Power Series And Linear Systems Of Meromorphic Ordinary Differential Equations
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Author : Werner Balser
language : en
Publisher: Springer Science & Business Media
Release Date : 2000
Formal Power Series And Linear Systems Of Meromorphic Ordinary Differential Equations written by Werner Balser 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 2000 with Mathematics categories.
Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a formal solution of a certain form, which can be relatively easily computed, but which generally involves such power series diverging everywhere. In this book the author presents the classical theory of meromorphic systems of ODE in the new light shed upon it by the recent achievements in the theory of summability of formal power series.
Entire And Meromorphic Functions
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Author : Lee A. Rubel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Entire And Meromorphic Functions written by Lee A. Rubel 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.
Mathematics is a beautiful subject, and entire functions is its most beautiful branch. Every aspect of mathematics enters into it, from analysis, algebra, and geometry all the way to differential equations and logic. For example, my favorite theorem in all of mathematics is a theorem of R. NevanJinna that two functions, meromorphic in the whole complex plane, that share five values must be identical. For real functions, there is nothing that even remotely corresponds to this. This book is an introduction to the theory of entire and meromorphic functions, with a heavy emphasis on Nevanlinna theory, otherwise known as value-distribution theory. Things included here that occur in no other book (that we are aware of) are the Fourier series method for entire and mero morphic functions, a study of integer valued entire functions, the Malliavin Rubel extension of Carlson's Theorem (the "sampling theorem"), and the first-order theory of the ring of all entire functions, and a final chapter on Tarski's "High School Algebra Problem," a topic from mathematical logic that connects with entire functions. This book grew out of a set of classroom notes for a course given at the University of Illinois in 1963, but they have been much changed, corrected, expanded, and updated, partially for a similar course at the same place in 1993. My thanks to the many students who prepared notes and have given corrections and comments.
Diophantine Approximation On Linear Algebraic Groups
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Author : Michel Waldschmidt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Diophantine Approximation On Linear Algebraic Groups written by Michel Waldschmidt 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 2013-03-14 with Mathematics categories.
The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. Two chapters provide complete and simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.
A Polynomial Approach To Linear Algebra
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Author : Paul A. Fuhrmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-01
A Polynomial Approach To Linear Algebra written by Paul A. Fuhrmann 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 2012-10-01 with Mathematics categories.
A Polynomial Approach to Linear Algebra is a text which is heavily biased towards functional methods. In using the shift operator as a central object, it makes linear algebra a perfect introduction to other areas of mathematics, operator theory in particular. This technique is very powerful as becomes clear from the analysis of canonical forms (Frobenius, Jordan). It should be emphasized that these functional methods are not only of great theoretical interest, but lead to computational algorithms. Quadratic forms are treated from the same perspective, with emphasis on the important examples of Bezoutian and Hankel forms. These topics are of great importance in applied areas such as signal processing, numerical linear algebra, and control theory. Stability theory and system theoretic concepts, up to realization theory, are treated as an integral part of linear algebra. Finally there is a chapter on Hankel norm approximation for the case of scalar rational functions which allows the reader to access ideas and results on the frontier of current research.
Geometric Algebraic And Topological Methods For Quantum Field Theory Proceedings Of The 2013 Villa De Leyva Summer School
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Author : Alexander Cardona
language : en
Publisher: World Scientific
Release Date : 2016-09-06
Geometric Algebraic And Topological Methods For Quantum Field Theory Proceedings Of The 2013 Villa De Leyva Summer School written by Alexander Cardona and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-06 with Mathematics categories.
Based on lectures held at the 8th edition of the series of summer schools in Villa de Leyva since 1999, this book presents an introduction to topics of current interest at the interface of geometry, algebra, analysis, topology and theoretical physics. It is aimed at graduate students and researchers in physics or mathematics, and offers an introduction to the topics discussed in the two weeks of the summer school: operator algebras, conformal field theory, black holes, relativistic fluids, Lie groupoids and Lie algebroids, renormalization methods, spectral geometry and index theory for pseudo-differential operators.
Nevanlinna Theory And Complex Differential Equations
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Author : Ilpo Laine
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-01
Nevanlinna Theory And Complex Differential Equations written by Ilpo Laine and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-01 with Mathematics categories.
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
Linear Algebra For Control Theory
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Author : Paul Van Dooren
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Linear Algebra For Control Theory written by Paul Van Dooren 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.
During the past decade the interaction between control theory and linear algebra has been ever increasing, giving rise to new results in both areas. As a natural outflow of this research, this book presents information on this interdisciplinary area. The cross-fertilization between control and linear algebra can be found in subfields such as Numerical Linear Algebra, Canonical Forms, Ring-theoretic Methods, Matrix Theory, and Robust Control. This book's editors were challenged to present the latest results in these areas and to find points of common interest. This volume reflects very nicely the interaction: the range of topics seems very wide indeed, but the basic problems and techniques are always closely connected. And the common denominator in all of this is, of course, linear algebra. This book is suitable for both mathematicians and students.
System Theory The Schur Algorithm And Multidimensional Analysis
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Author : Daniel Alpay
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-28
System Theory The Schur Algorithm And Multidimensional Analysis written by Daniel Alpay 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 2007-06-28 with Mathematics categories.
This volume contains six peer-refereed articles written on the occasion of the workshop Operator theory, system theory and scattering theory: multidimensional generalizations and related topics, held at the Department of Mathematics of the Ben-Gurion University of the Negev in June, 2005. The book will interest a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
Interpolation Theory Systems Theory And Related Topics
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Author : Daniel Alpay
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Interpolation Theory Systems Theory And Related Topics written by Daniel Alpay and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume is dedicated to Harry Dym, a leading expert in operator theory, on the occasion of his sixtieth birthday. The book opens with an autobiographical sketch, a list of publications and a personal account of I. Gohberg on his collaboration with Harry Dym. The mathematical papers cover Krein space operator theory, Schur analysis and interpolation, several complex variables and Riemann surfaces, matrix theory, system theory, and differential equations and mathematical physics. The book is of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.