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A Course of Modern Analysis
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E T Whittaker
This classic text is known to and used by thousands of mathematicians and students of mathematics throughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principal transcendental functions.
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Complex Analysis
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Lars V Ahlfors, Ahlfors Lars
A standard source of information of functions of one complex variable, this text has retained its wide popularity in this field by being consistently rigorous without becoming needlessly concerned with advanced or overspecialized material. Difficult points have been clarified, the book has been reviewed for accuracy, and notations and terminology ...
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Complex Analysis Second Edition
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Joseph Bak, Donald J Newman
This unusually lively textbook on complex variables introduces the theory of analytic functions, explores its diverse applications and shows the reader how to harness its powerful techniques. "Complex Analysis" offers new and interesting motivations for classical results and introduces related topics that do not appear in this form in other texts. ...
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Theory of Functions
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Konrad Knopp
Full, rigorous demonstrations of the general foundations: integral theorems, series, the expansion of analytic functions.
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Analytic Function Theory
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Einar Hille
This famous work is a textbook that emphasizes the conceptual and historical continuity of analytic function theory. The second volume broadens from a textbook to a textbook-treatise, covering the 'canonical' topics (including elliptic functions, entire and meromorphic functions, as well as conformal mapping, etc.) and other topics nearer the ...
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From Divergent Power Series to Analytic Functions
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Werner Balser
Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummability, and as an application, contains a proof of the fact that all formal power series solutions of non-linear ...
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Complex Variables
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Francis J Flanigan
Contents include: Calculus in the Plane; Harmonic Functions in the Plane; Analytic Functions and Power series; Singular Points and Laurent Series; and much more. Many fine illustrations and numerous problems (with solutions). 1972 edition.
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Introduction to Circle Packing: The Theory of Discrete Analytic Functions
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Kenneth Stephenson
The topic of 'circle packing' was born of the computer age but takes its inspiration and themes from core areas of classical mathematics. A circle packing is a configuration of circles having a specified pattern of tangencies, as introduced by William Thurston in 1985. This book lays out their study, from first definitions to latest theory, ...
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Elementary Theory of Analytic Functions of One or Several Complex Variables
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by
Henri Cartan
Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.
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Bounded Analytic Functions
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John B Garnett
'This book is an account of the theory of Hardy spaces in one dimension, with emphasis on some of the exciting developments of the past two decades or so. The last seven of the ten chapters are devoted in the main to these recent developments. The motif of the theory of Hardy spaces is the interplay between real, complex, and abstract analysis. ...
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A Course in Arithmetic
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Jean-Pierre Serre
Serre's "A Course in Arithmetic" is a concentrated, modern introduction to basically three areas of number theory, quadratic forms, Dirichlet's density theorem, and modular forms. The first edition was very well accepted and is now one of the leading introductory texts on the advanced undergraduate or beginning graduate level. "...The book is ...
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The Equidistribution Theory of Holomorphic Curves
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Hung-Hsi Wu
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Normal Families
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Joel L Schiff
This is the first book devoted solely to the subject of normal families of analytic and meromorphic functions since the 1927 treatise of Paul Montel. A considerable body of research has evolved since then, and this text provides a comprehensive treatment of the entire theory. Since its inception early this century, the notion of a normal family ...
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A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions, with an Account of the Principal Transcendental Functions
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E T Whittaker
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A Primer of Real Analytic Functions
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Steven G Krantz
The subject of real analytic functions is one of the oldest in modern mathematics and is the wellspring of the theory of analysis, both real and complex. To date, there is no comprehensive book on the subject, yet the tools of the theory are widely used by mathematicians today. Key topics in the theory of real analytic functions that are covered ...
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The Logarithmic Integral: Volume 1
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Paul Koosis, Bela Bollobas (Editor), W Fulton (Editor)
The theme of this unique work, the logarithmic integral, lies athwart much of twentieth century analysis. It is a thread connecting many apparently separate parts of the subject, and so is a natural point at which to begin a serious study of real and complex analysis. Professor Koosis' aim is to show how, from simple ideas, one can build up an ...
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Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set
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Karsten Keller
This book is mainly devoted to the combinatorics of quadratic holomorphic dynamics. The conceptual kernel is a self-contained abstract counterpart of connected quadratic Julia sets which is built on Thurston's concept of a quadratic invariant lamination and on symbolic descriptions of the angle-doubling map. The theory obtained is illustrated in ...
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Uniform algebras
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Theodore W. Gamelin
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Sharp Real-Part Theorems: A Unified Approach
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Gershon Kresin, Vladimir Maz'ya, T Shaposhnikova (Translator)
This volume contains a coherent point of view on various sharp pointwise inequalities for analytic functions in a disk in terms of the real part of the function on the boundary circle or in the disk itself. Inequalities of this type are frequently used in the theory of entire functions and in the analytic number theory. Rich opportunities are ...
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Theorie Des Fonctions Algebriques
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Paul Appell, P. Fatou, Edouard Goursat
Presents the text in French.
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Analytic Capacity and Rational Approximation
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Lawrence Zalcman
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Elliptic Systems and Quasiconformal Mappings
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Heinrich Renelt
The primary aim of this text is to provide an explanation of those first order elliptic systems of partial differentiation equations in the plane whose solutions consist of the composition of an analytic function with a quasiconformal mapping. The text begins with an introductory chapter which covers necessary results on generalized derivatives, ...
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The Schwarz Function and Its Applications
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Philip J. Davis
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Analytic functions
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Marat Andreevich Evgrafov
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The Cauchy Method of Residues Theory and Applications
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Dragoslav S Mitrinovic, Jovan D Keckic
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