The Schwarz Lemma

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Publisher : Courier Dover Publications
ISBN 13 : 0486810976
Total Pages : 260 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis The Schwarz Lemma by : Sean Dineen

Download or read book The Schwarz Lemma written by Sean Dineen and published by Courier Dover Publications. This book was released on 2016-04-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduates and graduate students, this self-contained overview covers the classical Schwarz lemma, Poincaré distance on the unit disc, hyperbolic manifolds, holomorphic curvature, and the analytic Radon-Nikodym property. 1989 edition.

Function Theory of Several Complex Variables

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Publisher : American Mathematical Soc.
ISBN 13 : 0821827243
Total Pages : 586 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Function Theory of Several Complex Variables by : Steven George Krantz

Download or read book Function Theory of Several Complex Variables written by Steven George Krantz and published by American Mathematical Soc.. This book was released on 2001 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.

Schwarz-Pick Type Inequalities

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Publisher : Springer Science & Business Media
ISBN 13 : 3034600003
Total Pages : 162 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Schwarz-Pick Type Inequalities by : Farit G. Avkhadiev

Download or read book Schwarz-Pick Type Inequalities written by Farit G. Avkhadiev and published by Springer Science & Business Media. This book was released on 2009-04-05 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a unified representation of generalizations of the Schwarz Lemma. It examines key coefficient theorems of the last century and explains the connection between coefficient estimates and characteristics of the hyperbolic geometry in a domain.

The Schwarz Lemma

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Author :
Publisher : Courier Dover Publications
ISBN 13 : 0486801209
Total Pages : 260 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis The Schwarz Lemma by : Sean Dineen

Download or read book The Schwarz Lemma written by Sean Dineen and published by Courier Dover Publications. This book was released on 2016-04-21 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: Oxford: Clarendon Press, 1989.

Complex Analysis

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Publisher : Springer Science & Business Media
ISBN 13 : 0387216073
Total Pages : 508 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Complex Analysis by : Theodore W. Gamelin

Download or read book Complex Analysis written by Theodore W. Gamelin and published by Springer Science & Business Media. This book was released on 2013-11-01 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which are aimed at an upper division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces, with emphasis placed on the three geometries: spherical, euclidean, and hyperbolic. Throughout, exercises range from the very simple to the challenging. The book is based on lectures given by the author at several universities, including UCLA, Brown University, La Plata, Buenos Aires, and the Universidad Autonomo de Valencia, Spain.

Schwarz's Lemma from a Differential Geometric Viewpoint

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Publisher : World Scientific
ISBN 13 : 9814324787
Total Pages : 100 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Schwarz's Lemma from a Differential Geometric Viewpoint by : Kang-Tae Kim

Download or read book Schwarz's Lemma from a Differential Geometric Viewpoint written by Kang-Tae Kim and published by World Scientific. This book was released on 2011 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject matter in this volume is Schwarz's lemma which has become a crucial theme in many branches of research in mathematics for more than a hundred years to date. This volume of lecture notes focuses on its differential geometric developments by several excellent authors including, but not limited to, L Ahlfors, S S Chern, Y C Lu, S T Yau and H L Royden. This volume can be approached by a reader who has basic knowledge on complex analysis and Riemannian geometry. It contains major historic differential geometric generalizations on Schwarz's lemma and provides the necessary information while making the whole volume as concise as ever.

Schwarz's Lemma From A Differential Geometric Viewpoint

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Publisher : World Scientific
ISBN 13 : 9814462799
Total Pages : 100 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Schwarz's Lemma From A Differential Geometric Viewpoint by : Kang-tae Kim

Download or read book Schwarz's Lemma From A Differential Geometric Viewpoint written by Kang-tae Kim and published by World Scientific. This book was released on 2010-12-09 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject matter in this volume is Schwarz's Lemma which has become a crucial theme in many branches of research in mathematics for more than a hundred years to date. This volume of lecture notes focuses on its differential geometric developments by several excellent authors including, but not limited to, L Ahlfors, S S Chern, Y C Lu, S T Yau and H L Royden.This volume can be approached by a reader who has basic knowledge on complex analysis and Riemannian geometry. It contains major historic differential geometric generalizations on Schwarz's Lemma and provides the necessary information while making the whole volume as concise as ever.

Univalent Functions

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Publisher : Springer Science & Business Media
ISBN 13 : 9780387907956
Total Pages : 414 pages
Book Rating : 4.9/5 (79 download)

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Book Synopsis Univalent Functions by : P. L. Duren

Download or read book Univalent Functions written by P. L. Duren and published by Springer Science & Business Media. This book was released on 2001-07-02 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Complex Analysis

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Publisher : Springer Science & Business Media
ISBN 13 : 1475718713
Total Pages : 380 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Complex Analysis by : Serge Lang

Download or read book Complex Analysis written by Serge Lang and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. Somewhat more material has been included than can be covered at leisure in one term, to give opportunities for the instructor to exercise his taste, and lead the course in whatever direction strikes his fancy at the time. A large number of routine exercises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recom mend to anyone to look through them. More recent texts have empha sized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex anal ysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues. The systematic elementary development of formal and convergent power series was standard fare in the German texts, but only Cartan, in the more recent books, includes this material, which I think is quite essential, e. g. , for differential equations. I have written a short text, exhibiting these features, making it applicable to a wide variety of tastes. The book essentially decomposes into two parts.

Harmonic Function Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 1475781377
Total Pages : 266 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Harmonic Function Theory by : Sheldon Axler

Download or read book Harmonic Function Theory written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.

The Cauchy-Schwarz Master Class

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Publisher : Cambridge University Press
ISBN 13 : 9780521546775
Total Pages : 320 pages
Book Rating : 4.5/5 (467 download)

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Book Synopsis The Cauchy-Schwarz Master Class by : J. Michael Steele

Download or read book The Cauchy-Schwarz Master Class written by J. Michael Steele and published by Cambridge University Press. This book was released on 2004-04-26 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.

A Second Course in Complex Analysis

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Publisher : Courier Corporation
ISBN 13 : 048615193X
Total Pages : 257 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis A Second Course in Complex Analysis by : William A. Veech

Download or read book A Second Course in Complex Analysis written by William A. Veech and published by Courier Corporation. This book was released on 2014-08-04 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear, self-contained treatment of important areas in complex analysis, this text is geared toward upper-level undergraduates and graduate students. The material is largely classical, with particular emphasis on the geometry of complex mappings. Author William A. Veech, the Edgar Odell Lovett Professor of Mathematics at Rice University, presents the Riemann mapping theorem as a special case of an existence theorem for universal covering surfaces. His focus on the geometry of complex mappings makes frequent use of Schwarz's lemma. He constructs the universal covering surface of an arbitrary planar region and employs the modular function to develop the theorems of Landau, Schottky, Montel, and Picard as consequences of the existence of certain coverings. Concluding chapters explore Hadamard product theorem and prime number theorem.

A Course in Complex Analysis

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Publisher : Princeton University Press
ISBN 13 : 0691207585
Total Pages : 442 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis A Course in Complex Analysis by : Saeed Zakeri

Download or read book A Course in Complex Analysis written by Saeed Zakeri and published by Princeton University Press. This book was released on 2021-11-02 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This textbook is intended for a year-long graduate course on complex analysis, a branch of mathematical analysis that has broad applications, particularly in physics, engineering, and applied mathematics. Based on nearly twenty years of classroom lectures, the book is accessible enough for independent study, while the rigorous approach will appeal to more experienced readers and scholars, propelling further research in this field. While other graduate-level complex analysis textbooks do exist, Zakeri takes a distinctive approach by highlighting the geometric properties and topological underpinnings of this area. Zakeri includes more than three hundred and fifty problems, with problem sets at the end of each chapter, along with additional solved examples. Background knowledge of undergraduate analysis and topology is needed, but the thoughtful examples are accessible to beginning graduate students and advanced undergraduates. At the same time, the book has sufficient depth for advanced readers to enhance their own research. The textbook is well-written, clearly illustrated, and peppered with historical information, making it approachable without sacrificing rigor. It is poised to be a valuable textbook for graduate students, filling a needed gap by way of its level and unique approach"--

Lectures on Riemann Surfaces

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Publisher : Springer Science & Business Media
ISBN 13 : 1461259614
Total Pages : 262 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Lectures on Riemann Surfaces by : Otto Forster

Download or read book Lectures on Riemann Surfaces written by Otto Forster and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Münster. It provides a concise modern introduction to this rewarding subject, as well as presenting methods used in the study of complex manifolds in the special case of complex dimension one. From the reviews: "This book deserves very serious consideration as a text for anyone contemplating giving a course on Riemann surfaces."—-MATHEMATICAL REVIEWS

Schwarz Lemma for Analytic Functions of Two Complex Variables

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (134 download)

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Book Synopsis Schwarz Lemma for Analytic Functions of Two Complex Variables by : H. E. Rauch

Download or read book Schwarz Lemma for Analytic Functions of Two Complex Variables written by H. E. Rauch and published by . This book was released on 1946 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Holomorphic Morse Inequalities and Bergman Kernels

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Publisher : Springer Science & Business Media
ISBN 13 : 3764381159
Total Pages : 432 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Holomorphic Morse Inequalities and Bergman Kernels by : Xiaonan Ma

Download or read book Holomorphic Morse Inequalities and Bergman Kernels written by Xiaonan Ma and published by Springer Science & Business Media. This book was released on 2007-12-14 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines holomorphic Morse inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel. It opens perspectives on several active areas of research in complex, Kähler and symplectic geometry. A large number of applications are also included, such as an analytic proof of Kodaira's embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, compactification of complete Kähler manifolds of pinched negative curvature, Berezin-Toeplitz quantization, weak Lefschetz theorems, and asymptotics of the Ray-Singer analytic torsion.

Function Theory in the Unit Ball of Cn

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Publisher : Springer Science & Business Media
ISBN 13 : 1461380987
Total Pages : 449 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Function Theory in the Unit Ball of Cn by : W. Rudin

Download or read book Function Theory in the Unit Ball of Cn written by W. Rudin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: Around 1970, an abrupt change occurred in the study of holomorphic functions of several complex variables. Sheaves vanished into the back ground, and attention was focused on integral formulas and on the "hard analysis" problems that could be attacked with them: boundary behavior, complex-tangential phenomena, solutions of the J-problem with control over growth and smoothness, quantitative theorems about zero-varieties, and so on. The present book describes some of these developments in the simple setting of the unit ball of en. There are several reasons for choosing the ball for our principal stage. The ball is the prototype of two important classes of regions that have been studied in depth, namely the strictly pseudoconvex domains and the bounded symmetric ones. The presence of the second structure (i.e., the existence of a transitive group of automorphisms) makes it possible to develop the basic machinery with a minimum of fuss and bother. The principal ideas can be presented quite concretely and explicitly in the ball, and one can quickly arrive at specific theorems of obvious interest. Once one has seen these in this simple context, it should be much easier to learn the more complicated machinery (developed largely by Henkin and his co-workers) that extends them to arbitrary strictly pseudoconvex domains. In some parts of the book (for instance, in Chapters 14-16) it would, however, have been unnatural to confine our attention exclusively to the ball, and no significant simplifications would have resulted from such a restriction.