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Complex Analysis

Posted By: AvaxGenius
Complex Analysis

Complex Analysis by Serge Lang
English | PDF | 1993 | 468 Pages | ISBN : N/A | 23.2 MB

The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. The first half, more or less, can be used for a one-semester course addressed to undergraduates. The second half can be used for a second semester, at either level. Somewhat more material has been included than can be covered at leisure in one or two terms, to give opportunities for the instructor to exercise individual taste, and to lead the course in whatever directions strikes the instructor's fancy at the time as well as extra read­ ing material for students on their own. A large number of routine exer­ cises 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 recommend to anyone to look through them. More recent texts have emphasized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex analysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues.

Complex Analysis

Posted By: AvaxGenius
Complex Analysis

Complex Analysis by Serge Lang
English | PDF | 1999 | 498 Pages | ISBN : 0387985921 | 31.7 MB

The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. The first half, more or less, can be used for a one-semester course addressed to undergraduates. The second half can be used for a second semester, at either level. Somewhat more material has been included than can be covered at leisure in one or two terms, to give opportunities for the instructor to exercise individual taste, and to lead the course in whatever directions strikes the instructor's fancy at the time as well as extra read­ ing material for students on their own. A large number of routine exer­ cises 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 recommend to anyone to look through them. More recent texts have emphasized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex analysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues.

Topics in Complex Analysis

Posted By: AvaxGenius
Topics in Complex Analysis

Topics in Complex Analysis by Dan Romik
English | PDF EPUB | 2023 | 308 Pages | ISBN : 3110796783 | 38.2 MB

This graduate-level mathematics textbook provides an in-depth and readable exposition of selected topics in complex analysis. The material spans both the standard theory at a level suitable for a first-graduate class on the subject and several advanced topics delving deeper into the subject and applying the theory in different directions. The focus is on beautiful applications of complex analysis to geometry and number theory. The text is accompanied by beautiful figures illustrating many of the concepts and proofs.

Complex Analysis

Posted By: AvaxGenius
Complex Analysis

Complex Analysis by Taras Mel'nyk
English | PDF EPUB (True) | 2023 | 252 Pages | ISBN : 3031396146 | 33 MB

Today, the theory of complex-valued functions finds widespread applications in various areas of mathematical research, as well as in electrical and mechanical engineering, aeronautics, and other disciplines. Complex analysis has become a basic course in mathematics, physics, and select engineering departments.

Approximation Theory: Moduli of Continuity and Global Smoothness Preservation

Posted By: AvaxGenius
Approximation Theory: Moduli of Continuity and Global Smoothness Preservation

Approximation Theory: Moduli of Continuity and Global Smoothness Preservation by George A. Anastassiou , Sorin G. Gal
English | PDF | 2000 | 520 Pages | ISBN : 0817641513 | 28.3 MB

We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties. To our knowledge it is the first time the entire calculus of moduli of smoothness has been included in a book. We then present numerous applications of Approximation Theory, giving exact val­ ues of errors in explicit forms. The K-functional method is systematically avoided since it produces nonexplicit constants. All other related books so far have allocated very little space to the computational aspect of moduli of smoothness. In Part II, we study/examine the Global Smoothness Preservation Prop­ erty (GSPP) for almost all known linear approximation operators of ap­ proximation theory including: trigonometric operators and algebraic in­ terpolation operators of Lagrange, Hermite-Fejer and Shepard type, also operators of stochastic type, convolution type, wavelet type integral opera­ tors and singular integral operators, etc. We present also a sufficient general theory for GSPP to hold true. We provide a great variety of applications of GSPP to Approximation Theory and many other fields of mathemat­ ics such as Functional analysis, and outside of mathematics, fields such as computer-aided geometric design (CAGD). Most of the time GSPP meth­ ods are optimal. Various moduli of smoothness are intensively involved in Part II. Therefore, methods from Part I can be used to calculate exactly the error of global smoothness preservation. It is the first time in the literature that a book has studied GSPP.

Value Distribution Theory and Related Topics

Posted By: AvaxGenius
Value Distribution Theory and Related Topics

Value Distribution Theory and Related Topics by G. Barsegian, I. Laine, C. C. Yang
English | PDF (True) | 2004 | 331 Pages | ISBN : 1402079508 | 34.1 MB

The Nevanlinna theory of value distribution of meromorphic functions, one of the milestones of complex analysis during the last century, was c- ated to extend the classical results concerning the distribution of of entire functions to the more general setting of meromorphic functions. Later on, a similar reasoning has been applied to algebroid functions, subharmonic functions and meromorphic functions on Riemann surfaces as well as to - alytic functions of several complex variables, holomorphic and meromorphic mappings and to the theory of minimal surfaces. Moreover, several appli- tions of the theory have been exploited, including complex differential and functional equations, complex dynamics and Diophantine equations. The main emphasis of this collection is to direct attention to a number of recently developed novel ideas and generalizations that relate to the - velopment of value distribution theory and its applications. In particular, we mean a recent theory that replaces the conventional consideration of counting within a disc by an analysis of their geometric locations. Another such example is presented by the generalizations of the second main theorem to higher dimensional cases by using the jet theory. Moreover, s- ilar ideas apparently may be applied to several related areas as well, such as to partial differential equations and to differential geometry. Indeed, most of these applications go back to the problem of analyzing zeros of certain complex or real functions, meaning in fact to investigate level sets or level surfaces.

Differential Geometry and Complex Analysis: A Volume Dedicated to the Memory of Harry Ernest Rauch

Posted By: AvaxGenius
Differential Geometry and Complex Analysis: A Volume Dedicated to the Memory of Harry Ernest Rauch

Differential Geometry and Complex Analysis: A Volume Dedicated to the Memory of Harry Ernest Rauch by Isaac Chavel, Hershel M. Farkas
English | PDF | 1985 | 228 Pages | ISBN : 3642698301 | 12.7 MB

This volume is dedicated to the memory of Harry Ernest Rauch, who died suddenly on June 18, 1979. In organizing the volume we solicited: (i) articles summarizing Rauch's own work in differential geometry, complex analysis and theta functions (ii) articles which would give the reader an idea of the depth and breadth of Rauch's researches, interests, and influence, in the fields he investigated, and (iii) articles of high scientific quality which would be of general interest. In each of the areas to which Rauch made significant contribution - pinching theorems, teichmiiller theory, and theta functions as they apply to Riemann surfaces - there has been substantial progress.

Classical Complex Analysis: A Geometric Approach, Volume 1 & 2

Posted By: roxul
Classical Complex Analysis: A Geometric Approach, Volume 1 & 2

I-Hsiung Lin, "Classical Complex Analysis: A Geometric Approach, Volume 1 & 2 "
English | ISBN: 981426122X, 9814271292 | 2010 | 1790 pages | PDF | 105 MB

Complex Analysis and Geometry

Posted By: AvaxGenius
Complex Analysis and Geometry

Complex Analysis and Geometry by Vincenzo Ancona, Alessandro Silva
English | PDF | 1993 | 418 Pages | ISBN : 0306441799 | 27.8 MB

When we studied complex variables in the late 1960s, modem geometry on the complex fie1d and complex function theory were identified in teaching and research as several complex variables. A beginner in the field at that time would have the experience of jumping from the sheaf-theoretical methods employed in the theory of analytic spaces to the P.D.E. methods of the ä- problem, with the c1ear understanding that the phenomena lying behind such different methods and problems were the same.

Frontiers of Fractal Analysis : Recent Advances and Challenges

Posted By: readerXXI
Frontiers of Fractal Analysis : Recent Advances and Challenges

Frontiers of Fractal Analysis : Recent Advances and Challenges
by Santo Banerjee and A. Gowrisankar
English | 2022 | ISBN: 103213867X | 174 Pages | True ePUB | 7.84 MB

Complex Analysis and Special Topics in Harmonic Analysis

Posted By: AvaxGenius
Complex Analysis and Special Topics in Harmonic Analysis

Complex Analysis and Special Topics in Harmonic Analysis by Carlos A. Berenstein, Roger Gay
English | PDF | 1995 | 491 Pages | ISBN : 1461384478 | 37.3 MB

A companion volume to the text "Complex Variables: An Introduction" by the same authors, this book further develops the theory, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis. Topics considered include: Boundary values of holomorphic functions in the sense of distributions; interpolation problems and ideal theory in algebras of entire functions with growth conditions; exponential polynomials; the G transform and the unifying role it plays in complex analysis and transcendental number theory; summation methods; and the theorem of L. Schwarz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic function theory.

Modern Real and Complex Analysis

Posted By: AvaxGenius
Modern Real and Complex Analysis

Modern Real and Complex Analysis by Bernard R. Gelbaum
English | PDF | 1995 | 496 Pages | ISBN : 0471107158 | 20 MB

Thorough, well-written, and encyclopedic in its coverage, this text offers a lucid presentation of all the topics essential to graduate study in analysis. While maintaining the strictest standards of rigor, Professor Gelbaum's approach is designed to appeal to intuition whenever possible. Modern Real and Complex Analysis provides up-to-date treatment of such subjects as the Daniell integration, differentiation, functional analysis and Banach algebras, conformal mapping and Bergman's kernels, defective functions, Riemann surfaces and uniformization, and the role of convexity in analysis. The text supplies an abundance of exercises and illustrative examples to reinforce learning, and extensive notes and remarks to help clarify important points.

Introduction to Complex Analysis

Posted By: AvaxGenius
Introduction to Complex Analysis

Introduction to Complex Analysis by E. M. Chirka, P. Dolbeault, G. M. Khenkin, A. G. Vitushkin
English | PDF | 1997 | 252 Pages | ISBN : 3540630058 | 22.5 MB

From the reviews of the first printing, published as Volume 7 of the Encyclopaedia of Mathematical Sciences:
"…… In this volume, we find an introductory essay entitled "Remarkable Facts of Complex Analysis" by Vitushkin… This is followed by articles by G.M.Khenkin on integral formulas in complex analysis, by E.M.Chirka on complex analytic sets, by Vitushkin on the geometry of hypersurfaces and by P.Dolbeault, on the theory of residues in several variables. … In sum, the volume under review is the first quarter of an important work that surveys an active branch of modern mathematics. Some of the individual articles are reminiscent in style of the early volumes of the first Ergebnisse series and will probably prove to be equally useful as a reference; all contain substantial lists of references."
Bulletin of the American Mathematical Society, 1991 "… This remarkable book has a helpfully informal style, abundant motivation, outlined proofs followed by precise references, and an extensive bibliography; it will be an invaluable reference and a companion to modern courses on several complex variables."

Complex Analysis I: Entire and Meromorphic Functions Polyanalytic Functions and Their Generalizations

Posted By: AvaxGenius
Complex Analysis I: Entire and Meromorphic Functions Polyanalytic Functions and Their Generalizations

Complex Analysis I: Entire and Meromorphic Functions Polyanalytic Functions and Their Generalizations by A. A. Gonchar, V. P. Havin, N. K. Nikolski
English | PDF | 1997 | 268 Pages | ISBN : 3540547037 | 24.5 MB

The first part of the volume contains a comprehensive description of the theory of entire and meromorphic functions of one complex variable and its applications. It includes the fundamental notions, methods and results on the growth of entire functions and the distribution of their zeros, the Rolf Nevanlinna theory of distribution of values of meromorphic functions including the inverse problem, the theory of completely regular growth, the concept of limit sets for entire and subharmonic functions.

Several Complex Variables VII: Sheaf-Theoretical Methods in Complex Analysis

Posted By: AvaxGenius
Several Complex Variables VII: Sheaf-Theoretical Methods in Complex Analysis

Several Complex Variables VII: Sheaf-Theoretical Methods in Complex Analysis by H. Grauert, Th. Peternell, R. Remmert
English | PDF | 1994 | 374 Pages | ISBN : 3540562591 | 32.9 MB

Of making many books there is no end; and much study is a weariness of the flesh. Eccl. 12.12. 1. In the beginning Riemann created the surfaces. The periods of integrals of abelian differentials on a compact surface of genus 9 immediately attach a g­ dimensional complex torus to X. If 9 ~ 2, the moduli space of X depends on 3g - 3 complex parameters. Thus problems in one complex variable lead, from the very beginning, to studies in several complex variables. Complex tori and moduli spaces are complex manifolds, i.e. Hausdorff spaces with local complex coordinates Z 1, … , Zn; holomorphic functions are, locally, those functions which are holomorphic in these coordinates. th In the second half of the 19 century, classical algebraic geometry was born in Italy. The objects are sets of common zeros of polynomials. Such sets are of finite dimension, but may have singularities forming a closed subset of lower dimension; outside of the singular locus these zero sets are complex manifolds.