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Analytic Function Theory Volume I

Analytic Function Theory  Volume I Author Einar Hille
ISBN-10 9780821875681
Release 2012-04-11
Pages 308
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Second Edition. 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 expanding frontier of analytic function theory. In the latter category are the chapters on majorization and on functions holomorphic in a half-plane.



Analytic Function Theory

Analytic Function Theory Author Einar Hille
ISBN-10 0821829149
Release 2005-03-23
Pages 496
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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 expanding frontier of analytic function theory. In the latter category are the chapters on majorization and on functions holomorphic in a half-plane.



Conformal Invariants

Conformal Invariants Author Lars Valerian Ahlfors
ISBN-10 9780821852705
Release 2010-11-17
Pages 160
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Most conformal invariants can be described in terms of extremal properties. Conformal invariants and extremal problems are therefore intimately linked and form together the central theme of this classic book which is primarily intended for students with approximately a year's background in complex variable theory. The book emphasizes the geometric approach as well as classical and semi-classical results which Lars Ahlfors felt every student of complex analysis should know before embarking on independent research. At the time of the book's original appearance, much of this material had never appeared in book form, particularly the discussion of the theory of extremal length. Schiffer's variational method also receives special attention, and a proof of $\vert a_4\vert \leq 4$ is included which was new at the time of publication. The last two chapters give an introduction to Riemann surfaces, with topological and analytical background supplied to support a proof of the uniformization theorem. Included in this new reprint is a Foreword by Peter Duren, F. W. Gehring, and Brad Osgood, as well as an extensive errata. ... encompasses a wealth of material in a mere one hundred and fifty-one pages. Its purpose is to present an exposition of selected topics in the geometric theory of functions of one complex variable, which in the author's opinion should be known by all prospective workers in complex analysis. From a methodological point of view the approach of the book is dominated by the notion of conformal invariant and concomitantly by extremal considerations. ... It is a splendid offering. --Reviewed for Math Reviews by M. H. Heins in 1975



Theory of Functions of a Complex Variable

Theory of Functions of a Complex Variable Author A. I. Markushevich
ISBN-10 9780821837801
Release 2005
Pages 1138
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Theorems are presented in a logical way and are carefully proved, making this a most useful book for students. --Choice This magnificent textbook, translated from the Russian, was first published in 1965-1967. The book covers all aspects of the theory of functions of one complex variable. The chosen proofs give the student the best `feel' for the subject. The watchwords are clarity and straightforwardness. The author was a leading Soviet function-theorist: It is seldom that an expert of his stature puts himself so wholly at the service of the student. This book includes over 150 illustrations and 700 exercises.



Harmonic and Complex Analysis and its Applications

Harmonic and Complex Analysis and its Applications Author Alexander Vasiliev
ISBN-10 9783319018065
Release 2013-11-09
Pages 358
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This volume highlights the main results of the research performed within the network “Harmonic and Complex Analysis and its Applications” (HCAA), which was a five-year (2007–2012) European Science Foundation Programme intended to explore and to strengthen the bridge between two scientific communities: analysts with broad backgrounds in complex and harmonic analysis and mathematical physics, and specialists in physics and applied sciences. It coordinated actions for advancing harmonic and complex analysis and for expanding its application to challenging scientific problems. Particular topics considered by this Programme included conformal and quasiconformal mappings, potential theory, Banach spaces of analytic functions and their applications to the problems of fluid mechanics, conformal field theory, Hamiltonian and Lagrangian mechanics, and signal processing. This book is a collection of surveys written as a result of activities of the Programme and will be interesting and useful for professionals and novices in analysis and mathematical physics, as well as for graduate students. Browsing the volume, the reader will undoubtedly notice that, as the scope of the Programme is rather broad, there are many interrelations between the various contributions, which can be regarded as different facets of a common theme.



Theory of Functions of a Complex Variable

Theory of Functions of a Complex Variable Author C. Caratheodory
ISBN-10 9780821828311
Release 2001
Pages 304
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This book is a translation by F. Steinhardt of the last of Caratheodory's celebrated text books, Funktiontheorie, Volume 1.



Function Theory of Several Complex Variables

Function Theory of Several Complex Variables Author Steven George Krantz
ISBN-10 9780821827246
Release 2001
Pages 564
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The theory of several complex variables can be studied from several different perspectives. In this book, Steven Krantz approaches the subject from the point of view of a classical analyst, emphasizing its function-theoretic aspects. He has taken particular care to write the book with the student in mind, with uniformly extensive and helpful explanations, numerous examples, and plentiful exercises of varying difficulty. In the spirit of a student-oriented text, Krantz begins with an introduction to the subject, including an insightful comparison of analysis of several complex variables with the more familiar theory of one complex variable. The main topics in the book include integral formulas, convexity and pseudoconvexity, methods from harmonic analysis, and several aspects of the $\overline{\partial}$ problem. Some further topics are zero sets of holomorphic functions, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and holomorphic mappings. While due attention is paid to algebraic aspects of several complex variables (sheaves, Cousin problems, etc.), the student with a background in real and complex variable theory, harmonic analysis, and differential equations will be most comfortable with this treatment. This book is suitable for a first graduate course in several complex variables.



Evolution Equations

Evolution Equations Author Kaïs Ammari
ISBN-10 9781108329590
Release 2017-10-05
Pages
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The proceedings of the summer school held at the Université Savoie Mont Blanc, France, 'Mathematics in Savoie 2015', whose theme was long time behavior and control of evolution equations. The event was attended by world-leading researchers from the community of control theory, as well as young researchers from around the globe. This volume contains surveys of active research topics, along with original research papers containing exciting new results on the behavior of evolution equations. It will therefore benefit both graduate students and researchers. Key topics include the recent view on the controllability of parabolic systems that permits the reader to overview the moment method for parabolic equations, as well as numerical stabilization and control of partial differential equations.



Modular Functions in Analytic Number Theory

Modular Functions in Analytic Number Theory Author Marvin Isadore Knopp
ISBN-10 0821844881
Release 2008-01-01
Pages 154
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Knopp's engaging book presents an introduction to modular functions in number theory by concentrating on two modular functions, $\eta(\tau)$ and $\vartheta(\tau)$, and their applications to two number-theoretic functions, $p(n)$ and $r_s(n)$. They are well chosen, as at the heart of these particular applications to the treatment of these specific number-theoretic functions lies the general theory of automorphic functions, a theory of far-reaching significance with important connections to a great many fields of mathematics. The book is essentially self-contained, assuming only a good first-year course in analysis. The excellent exposition presents the beautiful interplay between modular forms and number theory, making the book an excellent introduction to analytic number theory for a beginning graduate student.



Analytic Functions of Several Complex Variables

Analytic Functions of Several Complex Variables Author Robert Clifford Gunning
ISBN-10 9780821821657
Release 2009
Pages 317
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The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. After initial successes by Poincare and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable. Beginning in the 1930s, initially through the work of Oka, then H. Cartan, and continuing with the work of Grauert, Remmert, and others, new tools were introduced into the theory of several complex variables that resolved many of the open problems and fundamentally changed the landscape of the subject. These tools included a central role for sheaf theory and increased uses of topology and algebra. The book by Gunning and Rossi was the first of the modern era of the theory of several complex variables, which is distinguished by the use of these methods. The intention of Gunning and Rossi's book is to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces. Fundamental concepts and techniques are discussed as early as possible. The first chapter covers material suitable for a one-semester graduate course, presenting many of the central problems and techniques, often in special cases. The later chapters give more detailed expositions of sheaf theory for analytic functions and the theory of complex analytic spaces. Since its original publication, this book has become a classic resource for the modern approach to functions of several complex variables and the theory of analytic spaces. Further information about this book, including updates, can be found at the following URL: www.ams.org/bookpages/chel-368.



An Introduction to Multicomplex SPates and Functions

An Introduction to Multicomplex SPates and Functions Author Price
ISBN-10 9781351467087
Release 2018-05-11
Pages 424
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A rather pretty little book, written in the form of a text but more likely to be read simply for pleasure, in which the author (Professor Emeritus of Mathematics at the U. of Kansas) explores the analog of the theory of functions of a complex variable which comes into being when the complexes are re



Analytic Combinatorics in Several Variables

Analytic Combinatorics in Several Variables Author Robin Pemantle
ISBN-10 9781107031579
Release 2013-05-31
Pages 380
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This book is the result of nearly fifteen years of work on developing analytic machinery to recover, as effectively as possible, asymptotics of the coefficients of a multivariate generating function. It is the first book to describe many of the results and techniques necessary to estimate coefficients of generating functions in more than one variable.



Complex Manifolds

Complex Manifolds Author James A. Morrow
ISBN-10 9780821840559
Release 1971
Pages 194
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This volume serves as an introduction to the Kodaira-Spencer theory of deformations of complex structures. Based on notes taken by James Morrow from lectures given by Kunihiko Kodaira at Stanford University in 1965-1966, the book gives the original proof of the Kodaira embedding theorem, showing that the restricted class of Kahler manifolds called Hodge manifolds is algebraic. Included are the semicontinuity theorems and the local completeness theorem of Kuranishi. Readers are assumed to know some algebraic topology. Complete references are given for the results that are used from elliptic partial differential equations. The book is suitable for graduate students and researchers interested in abstract complex manifolds.



Ordinary Differential Equations in the Complex Domain

Ordinary Differential Equations in the Complex Domain Author Einar Hille
ISBN-10 0486696200
Release 1997
Pages 484
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Graduate-level text offers full treatments of existence theorems, representation of solutions by series, theory of majorants, dominants and minorants, questions of growth, much more. Includes 675 exercises. Bibliography.



An Introduction to Complex Analysis in Several Variables

An Introduction to Complex Analysis in Several Variables Author L. Hormander
ISBN-10 9780444105233
Release 1973-02-12
Pages 213
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An Introduction to Complex Analysis in Several Variables



Automorphic Functions

Automorphic Functions Author Lester R. Ford
ISBN-10 0821837419
Release 1951
Pages 333
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Lester Ford's book was the first treatise in English on automorphic functions. At the time of its publication (1929), it was welcomed for its elegant treatment of groups of linear transformations and for the remarkably clear and explicit exposition throughout the book. Ford's extraordinary talent for writing has been memorialized in the prestigious award that bears his name. The book, in the meantime, has become a recognized classic. Ford's approach is primarily through analytic function theory. The first part of the book covers groups of linear transformations, especially Fuchsian groups, fundamental domains, and functions that are invariant under the groups, including the classical elliptic modular functions and Poincare theta series. The second part of the book covers conformal mappings, uniformization, and connections between automorphic functions and differential equations with regular singular points, such as the hypergeometric equation.



Introduction to Holomorphic Functions of Several Variables Homological theory

Introduction to Holomorphic Functions of Several Variables  Homological theory Author Robert Clifford Gunning
ISBN-10 053413310X
Release 1990-09-01
Pages 216
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Introduction to Holomorphic Functions of Several Variables Homological theory has been writing in one form or another for most of life. You can find so many inspiration from Introduction to Holomorphic Functions of Several Variables Homological theory also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Introduction to Holomorphic Functions of Several Variables Homological theory book for free.