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Potential Theory in the Complex Plane

Potential Theory in the Complex Plane Author Thomas Ransford
ISBN-10 0521466547
Release 1995-03-16
Pages 232
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Ransford provides an introduction to the subject, concentrating on the important case of two dimensions, and emphasizing its links with complex analysis. This is reflected in the large number of applications, which include Picard's theorem, the Phragmén-Lindelöf principle, the Radó-Stout theorem, Lindelöf's theory of asymptotic values, the Riemann mapping theorem (including continuity at the boundary), the Koebe one-quarter theorem, Hilbert's lemniscate theorem, and the sharp quantitative form of Runge's theorem. In addition, there is a chapter on connections with functional analysis and dynamical systems, which shows how the theory can be applied to other parts of mathematics and gives a flavor of some recent research in the area.



Potential Theory and Dynamics on the Berkovich Projective Line

Potential Theory and Dynamics on the Berkovich Projective Line Author Matthew Baker
ISBN-10 9780821849248
Release 2010-03-10
Pages 428
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The purpose of this book is to develop the foundations of potential theory and rational dynamics on the Berkovich projective line over an arbitrary complete, algebraically closed non-Archimedean field. In addition to providing a concrete and ``elementary'' introduction to Berkovich analytic spaces and to potential theory and rational iteration on the Berkovich line, the book contains applications to arithmetic geometry and arithmetic dynamics. A number of results in the book are new, and most have not previously appeared in book form. Three appendices--on analysis, $\mathbb{R}$-trees, and Berkovich's general theory of analytic spaces--are included to make the book as self-contained as possible. The authors first give a detailed description of the topological structure of the Berkovich projective line and then introduce the Hsia kernel, the fundamental kernel for potential theory. Using the theory of metrized graphs, they define a Laplacian operator on the Berkovich line and construct theories of capacities, harmonic and subharmonic functions, and Green's functions, all of which are strikingly similar to their classical complex counterparts. After developing a theory of multiplicities for rational functions, they give applications to non-Archimedean dynamics, including local and global equidistribution theorems, fixed point theorems, and Berkovich space analogues of many fundamental results from the classical Fatou-Julia theory of rational iteration. They illustrate the theory with concrete examples and exposit Rivera-Letelier's results concerning rational dynamics over the field of $p$-adic complex numbers. They also establish Berkovich space versions of arithmetic results such as the Fekete-Szego theorem and Bilu's equidistribution theorem.



Modern Trends in Constructive Function Theory

Modern Trends in Constructive Function Theory Author E. B. Saff
ISBN-10 9781470425340
Release 2016-03-31
Pages 297
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This volume contains the proceedings of the conference Constructive Functions 2014, held from May 26-30, 2014, at Vanderbilt University, Nashville, TN, in honor of Ed Saff's 70th birthday. The papers in this volume contain results on polynomial approximation, rational approximation, Log-optimal configurations on the sphere, random continued fractions, ratio asymptotics for multiple orthogonal polynomials, the bivariate trigonometric moment problem, minimal Riesz energy, random polynomials, Pade and Hermite-Pade approximation, orthogonal expansions, hyperbolic differential equations, Bergman polynomials, the Meijer $G$-function, polynomial ensembles, and integer lattice points.



Introduction to Banach Spaces and Algebras

Introduction to Banach Spaces and Algebras Author Graham R. Allan
ISBN-10 9780199206537
Release 2011
Pages 371
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A graduate level text in functional analysis, with an emphasis on Banach algebras. Based on lectures given for Part III of the Cambridge Mathematical Tripos, the text will assume a familiarity with elementary real and complex analysis, and some acquaintance with metric spaces, analytic topology and normed spaces (but not theorems depending on Baire category, or any version of the Hahn-Banach theorem).



Invariant Distances and Metrics in Complex Analysis

Invariant Distances and Metrics in Complex Analysis Author Marek Jarnicki
ISBN-10 9783110253863
Release 2013-06-26
Pages 878
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As in the field of "Invariant Distances and Metrics in Complex Analysis" there was and is a continuous progress this is the second extended edition of the corresponding monograph. This comprehensive book is about the study of invariant pseudodistances (non-negative functions on pairs of points) and pseudometrics (non-negative functions on the tangent bundle) in several complex variables. It is an overview over a highly active research area at the borderline between complex analysis, functional analysis and differential geometry. New chapters are covering the Wu, Bergman and several other metrics.



Undergraduate Algebraic Geometry

Undergraduate Algebraic Geometry Author Miles Reid
ISBN-10 0521356628
Release 1988-12-15
Pages 129
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This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time.



Dynamical Systems and Ergodic Theory

Dynamical Systems and Ergodic Theory Author Mark Pollicott
ISBN-10 0521575990
Release 1998-01-29
Pages 179
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This book is essentially a self-contained introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. Parts of the book are suitable for a final year undergraduate course or for a master's level course. A number of applications are given, principally to number theory and arithmetic progressions (through van der Waerden's theorem and Szemerdi's theorem).



Automorphisms of Surfaces After Nielsen and Thurston

Automorphisms of Surfaces After Nielsen and Thurston Author Andrew J. Casson
ISBN-10 0521349850
Release 1988
Pages 104
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A comprehensive introduction to selected aspects of modern low-dimensional topology for readers with a knowledge of basic algebra.



Complex Algebraic Curves

Complex Algebraic Curves Author Frances Clare Kirwan
ISBN-10 0521423538
Release 1992-02-20
Pages 264
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This development of the theory of complex algebraic curves was one of the peaks of nineteenth century mathematics. They have many fascinating properties and arise in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.



Representation Theorems in Hardy Spaces

Representation Theorems in Hardy Spaces Author Javad Mashreghi
ISBN-10 9780521517683
Release 2009-03-19
Pages 372
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This self-contained text provides an introduction to a wide range of representation theorems and provides a complete description of the representation theorems with direct proofs for both classes of Hardy spaces: Hardy spaces of the open unit disc and Hardy spaces of the upper half plane.



Set Theory

Set Theory Author A. Hajnal
ISBN-10 1107362555
Release 2014-05-14
Pages 325
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This is a classic introduction to set theory, from the basics through to the modern tools of combinatorial set theory.



Steps in Commutative Algebra

Steps in Commutative Algebra Author R. Y. Sharp
ISBN-10 0521646235
Release 2000
Pages 355
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This introductory account of commutative algebra is aimed at advanced undergraduates and first year graduate students. Assuming only basic abstract algebra, it provides a good foundation in commutative ring theory, from which the reader can proceed to more advanced works in commutative algebra and algebraic geometry. The style throughout is rigorous but concrete, with exercises and examples given within chapters, and hints provided for the more challenging problems used in the subsequent development. After reminders about basic material on commutative rings, ideals and modules are extensively discussed, with applications including to canonical forms for square matrices. The core of the book discusses the fundamental theory of commutative Noetherian rings. Affine algebras over fields, dimension theory and regular local rings are also treated, and for this second edition two further chapters, on regular sequences and Cohen–Macaulay rings, have been added. This book is ideal as a route into commutative algebra.



Complex Dynamics

Complex Dynamics Author Lennart Carleson
ISBN-10 9781461243649
Release 2013-11-11
Pages 192
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A discussion of the properties of conformal mappings in the complex plane, closely related to the study of fractals and chaos. Indeed, the book ends in a detailed study of the famous Mandelbrot set, which describes very general properties of such mappings. Focusing on the analytic side of this contemporary subject, the text was developed from a course taught over several semesters and aims to help students and instructors to familiarize themselves with complex dynamics. Topics covered include: conformal and quasi-conformal mappings, fixed points and conjugations, basic rational iteration, classification of periodic components, critical points and expanding maps, some applications of conformal mappings, the local geometry of the Fatou set, and quadratic polynomials and the Mandelbrot set.



The Prime Number Theorem

The Prime Number Theorem Author G. J. O. Jameson
ISBN-10 0521891108
Release 2003-04-17
Pages 252
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The prime numbers appear to be distributed in a very irregular way amongst the integers, but the prime number theorem provides a simple formula that tells us (in an approximate but well-defined sense) how many primes we can expect to find that are less than any integer we might choose. This is indisputably one of the the great classical theorems of mathematics. Suitable for advanced undergraduates and beginning graduates, this textbook demonstrates how the tools of analysis can be used in number theory to attack a famous problem.



Proceedings

Proceedings Author
ISBN-10 UCSD:31822036334803
Release 2009
Pages
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Proceedings has been writing in one form or another for most of life. You can find so many inspiration from Proceedings also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Proceedings book for free.



Mathematics of Computation

Mathematics of Computation Author
ISBN-10 UCSD:31822035033281
Release 2006
Pages
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Mathematics of Computation has been writing in one form or another for most of life. You can find so many inspiration from Mathematics of Computation also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mathematics of Computation book for free.



SIAM Journal on Applied Mathematics

SIAM Journal on Applied Mathematics Author
ISBN-10 UCSD:31822022692321
Release
Pages
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SIAM Journal on Applied Mathematics has been writing in one form or another for most of life. You can find so many inspiration from SIAM Journal on Applied Mathematics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full SIAM Journal on Applied Mathematics book for free.