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Author: KRANTZ
Publisher: Birkhäuser
ISBN: 3034876440
Category : Science
Languages : en
Pages : 190
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Book Description
The subject of real analytic functions is one of the oldest in mathe matical analysis. Today it is encountered early in ones mathematical training: the first taste usually comes in calculus. While most work ing mathematicians use real analytic functions from time to time in their work, the vast lore of real analytic functions remains obscure and buried in the literature. It is remarkable that the most accessible treatment of Puiseux's theorem is in Lefschetz's quite old Algebraic Geometry, that the clearest discussion of resolution of singularities for real analytic manifolds is in a book review by Michael Atiyah, that there is no comprehensive discussion in print of the embedding prob lem for real analytic manifolds. We have had occasion in our collaborative research to become ac quainted with both the history and the scope of the theory of real analytic functions. It seems both appropriate and timely for us to gather together this information in a single volume. The material presented here is of three kinds. The elementary topics, covered in Chapter 1, are presented in great detail. Even results like a real ana lytic inverse function theorem are difficult to find in the literature, and we take pains here to present such topics carefully. Topics of middling difficulty, such as separate real analyticity, Puiseux series, the FBI transform, and related ideas (Chapters 2-4), are covered thoroughly but rather more briskly.
Author: KRANTZ
Publisher: Birkhäuser
ISBN: 3034876440
Category : Science
Languages : en
Pages : 190
Get Book
Book Description
The subject of real analytic functions is one of the oldest in mathe matical analysis. Today it is encountered early in ones mathematical training: the first taste usually comes in calculus. While most work ing mathematicians use real analytic functions from time to time in their work, the vast lore of real analytic functions remains obscure and buried in the literature. It is remarkable that the most accessible treatment of Puiseux's theorem is in Lefschetz's quite old Algebraic Geometry, that the clearest discussion of resolution of singularities for real analytic manifolds is in a book review by Michael Atiyah, that there is no comprehensive discussion in print of the embedding prob lem for real analytic manifolds. We have had occasion in our collaborative research to become ac quainted with both the history and the scope of the theory of real analytic functions. It seems both appropriate and timely for us to gather together this information in a single volume. The material presented here is of three kinds. The elementary topics, covered in Chapter 1, are presented in great detail. Even results like a real ana lytic inverse function theorem are difficult to find in the literature, and we take pains here to present such topics carefully. Topics of middling difficulty, such as separate real analyticity, Puiseux series, the FBI transform, and related ideas (Chapters 2-4), are covered thoroughly but rather more briskly.
Author: Springer
Publisher:
ISBN: 9780817681357
Category :
Languages : en
Pages : 224
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Book Description
Author: Steven George Krantz
Publisher: Birkhauser
ISBN: 9783764342647
Category : Analytic functions
Languages : en
Pages : 0
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Book Description
Author: Steven George Krantz
Publisher: Birkhauser
ISBN: 9783764327682
Category : Analytic functions
Languages : en
Pages : 184
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Book Description
Treats the subject of analytic functions of one or more real variables, using almost solely the techniques of real analysis, an approach that alters the usual progression of ideas and raises previously neglected questions. The beginning requires only a background in calculus, but the increasingly complex topics require increasing sophistication. Annotation copyright by Book News, Inc., Portland, OR
Author: John Ben Hough
Publisher: American Mathematical Soc.
ISBN: 0821843737
Category : Analytic functions
Languages : en
Pages : 170
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Book Description
Examines in some depth two important classes of point processes, determinantal processes and 'Gaussian zeros', i.e., zeros of random analytic functions with Gaussian coefficients. This title presents a primer on modern techniques on the interface of probability and analysis.
Author: Jeffrey Stopple
Publisher: Cambridge University Press
ISBN: 9780521012539
Category : Mathematics
Languages : en
Pages : 404
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Book Description
An undergraduate-level 2003 introduction whose only prerequisite is a standard calculus course.
Author: Bengt Fornberg
Publisher: SIAM
ISBN: 1611975980
Category : Mathematics
Languages : en
Pages : 371
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Book Description
At almost all academic institutions worldwide, complex variables and analytic functions are utilized in courses on applied mathematics, physics, engineering, and other related subjects. For most students, formulas alone do not provide a sufficient introduction to this widely taught material, yet illustrations of functions are sparse in current books on the topic. This is the first primary introductory textbook on complex variables and analytic functions to make extensive use of functional illustrations. Aiming to reach undergraduate students entering the world of complex variables and analytic functions, this book utilizes graphics to visually build on familiar cases and illustrate how these same functions extend beyond the real axis. It covers several important topics that are omitted in nearly all recent texts, including techniques for analytic continuation and discussions of elliptic functions and of Wiener–Hopf methods. It also presents current advances in research, highlighting the subject’s active and fascinating frontier. The primary audience for this textbook is undergraduate students taking an introductory course on complex variables and analytic functions. It is also geared toward graduate students taking a second semester course on these topics, engineers and physicists who use complex variables in their work, and students and researchers at any level who want a reference book on the subject.
Author: Ralph P. Boas
Publisher: American Mathematical Soc.
ISBN: 1470454327
Category :
Languages : en
Pages : 305
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Book Description
This is a revised, updated, and significantly augmented edition of a classic Carus Monograph (a bestseller for over 25 years) on the theory of functions of a real variable. Earlier editions of this classic Carus Monograph covered sets, metric spaces, continuous functions, and differentiable functions. The fourth edition adds sections on measurable sets and functions, the Lebesgue and Stieltjes integrals, and applications. The book retains the informal chatty style of the previous editions, remaining accessible to readers with some mathematical sophistication and a background in calculus. The book is, thus, suitable either for self-study or for supplemental reading in a course on advanced calculus or real analysis. Not intended as a systematic treatise, this book has more the character of a sequence of lectures on a variety of interesting topics connected with real functions. Many of these topics are not commonly encountered in undergraduate textbooks: e.g., the existence of continuous everywhere-oscillating functions (via the Baire category theorem); the universal chord theorem; two functions having equal derivatives, yet not differing by a constant; and application of Stieltjes integration to the speed of convergence of infinite series. This book recaptures the sense of wonder that was associated with the subject in its early days. It is a must for mathematics libraries.
Author: Derek K. Thomas
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110560968
Category : Mathematics
Languages : en
Pages : 265
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Book Description
The study of univalent functions dates back to the early years of the 20th century, and is one of the most popular research areas in complex analysis. This book is directed at introducing and bringing up to date current research in the area of univalent functions, with an emphasis on the important subclasses, thus providing an accessible resource suitable for both beginning and experienced researchers. Contents Univalent Functions – the Elementary Theory Definitions of Major Subclasses Fundamental Lemmas Starlike and Convex Functions Starlike and Convex Functions of Order α Strongly Starlike and Convex Functions Alpha-Convex Functions Gamma-Starlike Functions Close-to-Convex Functions Bazilevič Functions B1(α) Bazilevič Functions The Class U(λ) Convolutions Meromorphic Univalent Functions Loewner Theory Other Topics Open Problems
Author: Oscar Blasco
Publisher: American Mathematical Soc.
ISBN: 0821852752
Category : Analytic functions
Languages : en
Pages : 266
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Book Description
This book contains the lecture notes as well as some invited papers presented at the Third Winter School in Complex Analysis, Operator Theory and Applications held February 2-5, 2010, in Valencia, Spain. The book is divided into two parts. The first is an extended self-contained version of the mini-courses taught at the School. The papers in this first part are: Notes on real analytic functions and classical operators, by Pawel Domanski; Shining a Hilbertian lamp on the bidisk, by John E. McCarthy; Selected problems in perturbation theory, by Vladimir V. Peller; and Composition operators on Hardy-Orlicz spaces, by Luis Rodriguez-Piazza. The second part consists of several research papers on recent advances in the area and some survey articles of an expository character. The articles in this second part are: Remarks on weighted mixed norm spaces, by O. Blasco; Interpolation subspaces of $L^1$ of a vector measure and norm inequalities for the integration operator, by J.M. Calabuig, J. Rodriguez, and E.A. Sanchez-Perez; On the spectra of algebras of analytic functions, by D. Carando, D. Garcia, M. Maestre, and P. Sevilla-Peris; Holomorphic self-maps of the disk intertwining two linear fractional maps, by M.D. Contreras, S. Diaz-Madrigal, M.J. Martin, and D. Vukotic; ABC-type estimates via Garsia-type norms, by K.M. Dyakonov; and Volterra type operators on Bergman spaces with exponential weights, by J. Pau and J.A. Pelaez. The topics selected for the mini-courses cover several aspects of complex analysis and operator theory that play important roles in understanding connections between different areas that are considered in fashion these days. This part is aimed at graduate students and young researchers. The courses are self-contained, focusing on those aspects that are basic and that can lead the readers to a quick understanding of the theories presented in each topic. They start with the classical results and reach a selection of open problems in each case. The research and survey articles are aimed at young researchers in the area, as well as post-doc and senior researchers interested in complex analysis and operator theory. This book is published in cooperation with Real Sociedad Matematica Espanola.
