Generalized Analytic Functions on Riemann Surfaces PDF Download
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Author: Yuri L. Rodin
Publisher:
ISBN: 9783662195161
Category :
Languages : en
Pages : 140
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Book Description
Author: Yuri L. Rodin
Publisher:
ISBN: 9783662195161
Category :
Languages : en
Pages : 140
Get Book Here
Book Description
Author: I︠U︡riĭ Leonidovich Rodin
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 142
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Book Description
Author: Yuri L. Rodin
Publisher: Springer
ISBN: 3540480188
Category : Mathematics
Languages : en
Pages : 134
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Book Description
Author: Robert C. Gunning
Publisher: Springer Science & Business Media
ISBN: 3642663826
Category : Mathematics
Languages : en
Pages : 177
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Book Description
The investigation of the relationships between compact Riemann surfaces (al gebraic curves) and their associated complex tori (Jacobi varieties) has long been basic to the study both of Riemann surfaces and of complex tori. A Riemann surface is naturally imbedded as an analytic submanifold in its associated torus; and various spaces of linear equivalence elasses of divisors on the surface (or equivalently spaces of analytic equivalence elasses of complex line bundies over the surface), elassified according to the dimensions of the associated linear series (or the dimensions of the spaces of analytic cross-sections), are naturally realized as analytic subvarieties of the associated torus. One of the most fruitful of the elassical approaches to this investigation has been by way of theta functions. The space of linear equivalence elasses of positive divisors of order g -1 on a compact connected Riemann surface M of genus g is realized by an irreducible (g -1)-dimensional analytic subvariety, an irreducible hypersurface, of the associated g-dimensional complex torus J(M); this hyper 1 surface W- r;;;, J(M) is the image of the natural mapping Mg- -+J(M), and is g 1 1 birationally equivalent to the (g -1)-fold symmetric product Mg- jSg-l of the Riemann surface M.
Author: Lars Valerian Ahlfors
Publisher: Princeton University Press
ISBN: 140087453X
Category : Mathematics
Languages : en
Pages : 397
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Book Description
The theory of Riemann surfaces has a geometric and an analytic part. The former deals with the axiomatic definition of a Riemann surface, methods of construction, topological equivalence, and conformal mappings of one Riemann surface on another. The analytic part is concerned with the existence and properties of functions that have a special character connected with the conformal structure, for instance: subharmonic, harmonic, and analytic functions. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: Lars Valerian Ahlfors
Publisher: Princeton University Press
ISBN: 0691079390
Category : Mathematics
Languages : en
Pages : 275
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Book Description
A classic treatment of Riemann surfaces from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.
Author: Menahem Schiffer
Publisher: Princeton University Press
ISBN: 1400877520
Category : Mathematics
Languages : en
Pages : 462
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Book Description
An investigation of finite Riemann surfaces from the point of view of functional analysis, that is, the study of the various Abelian differentials of the surface in their dependence on the surface itself. Many new results are presented. Originally published in 1954. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: Helmut Florian
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 350
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Book Description
Contains papers from a January 1997 conference at the Technical University of Graz. Part I looks at generalized analytic functions, dealing not only with problems in the complex plane but also related problems in higher dimensions where several complex variables and Clifford Analysis are used. Part II is devoted to applications of partial differential equations to mechanics, with contributions on boundary elements and asymptotic methods, and hemivariational inequalities. A substantial number of papers in Part II deal with problems of ocean acoustics. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Rick Miranda
Publisher: American Mathematical Soc.
ISBN: 0821802682
Category : Mathematics
Languages : en
Pages : 414
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Book Description
In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking centre stage. But the main examples come fromprojective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Dualtiy Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves andcohomology are introduced as a unifying device in the later chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one term of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry.
Author: Dror Varolin
Publisher: American Mathematical Soc.
ISBN: 0821853694
Category : Mathematics
Languages : en
Pages : 258
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Book Description
This book establishes the basic function theory and complex geometry of Riemann surfaces, both open and compact. Many of the methods used in the book are adaptations and simplifications of methods from the theories of several complex variables and complex analytic geometry and would serve as excellent training for mathematicians wanting to work in complex analytic geometry. After three introductory chapters, the book embarks on its central, and certainly most novel, goal of studying Hermitian holomorphic line bundles and their sections. Among other things, finite-dimensionality of spaces of sections of holomorphic line bundles of compact Riemann surfaces and the triviality of holomorphic line bundles over Riemann surfaces are proved, with various applications. Perhaps the main result of the book is Hormander's Theorem on the square-integrable solution of the Cauchy-Riemann equations. The crowning application is the proof of the Kodaira and Narasimhan Embedding Theorems for compact and open Riemann surfaces. The intended reader has had first courses in real and complex analysis, as well as advanced calculus and basic differential topology (though the latter subject is not crucial). As such, the book should appeal to a broad portion of the mathematical and scientific community. This book is the first to give a textbook exposition of Riemann surface theory from the viewpoint of positive Hermitian line bundles and Hormander $\bar \partial$ estimates. It is more analytical and PDE oriented than prior texts in the field, and is an excellent introduction to the methods used currently in complex geometry, as exemplified in J. P. Demailly's online but otherwise unpublished book ``Complex analytic and differential geometry.'' I used it for a one quarter course on Riemann surfaces and found it to be clearly written and self-contained. It not only fills a significant gap in the large textbook literature on Riemann surfaces but is also rather indispensible for those who would like to teach the subject from a differential geometric and PDE viewpoint. --Steven Zelditch
