From Divergent Power Series to Analytic Functions

From Divergent Power Series to Analytic Functions PDF

Author: Werner Balser

Publisher: Springer

Published: 2006-11-15

Total Pages: 117

ISBN-13: 3540485945

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Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.

Analytic Combinatorics in Several Variables

Analytic Combinatorics in Several Variables PDF

Author: Robin Pemantle

Publisher: Cambridge University Press

Published: 2013-05-31

Total Pages: 395

ISBN-13: 1107031575

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Aimed at graduate students and researchers in enumerative combinatorics, this book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective.

A Primer of Real Analytic Functions

A Primer of Real Analytic Functions PDF

Author: KRANTZ

Publisher: Birkhäuser

Published: 2013-03-09

Total Pages: 190

ISBN-13: 3034876440

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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.

Tasty Bits of Several Complex Variables

Tasty Bits of Several Complex Variables PDF

Author: Jiri Lebl

Publisher: Lulu.com

Published: 2016-05-05

Total Pages: 142

ISBN-13: 1365095576

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This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014 and Spring 2016 semester at Oklahoma State University. The course covers basics of holomorphic function theory, CR geometry, the dbar problem, integral kernels and basic theory of complex analytic subvarieties. See http: //www.jirka.org/scv/ for more information.

Impeccability and Temptation

Impeccability and Temptation PDF

Author: Johannes Grössl

Publisher: Routledge

Published: 2021-04-13

Total Pages: 316

ISBN-13: 1000376656

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In Christian theology, the teaching that Christ possessed both a human and divine will is central to the doctrine of two natures, but it also represents a logical paradox, raising questions about how a person can be both impeccable and subject to temptation. This volume explores these questions through an analytic theology approach, bringing together 15 original papers that explore the implications of a strong libertarian concept of free will for Christology. With perspectives from systematic theologians, philosophers, and biblical scholars, several chapters also offer a comparative theology approach, examining the concept of impeccability in the Muslim tradition. Therefore, this volume will be of interest to scholars and graduate students working in analytic theology, biblical scholarship, systematic theology, and Christian-Islamic dialogue.

Analytic Functions

Analytic Functions PDF

Author: Rolf Nevanlinna

Publisher: Springer

Published: 2013-12-20

Total Pages: 383

ISBN-13: 3642855903

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The present monograph on analytic functions coincides to a lar[extent with the presentation of the modern theory of single-value analytic functions given in my earlier works "Le theoreme de Picarc Borel et la theorie des fonctions meromorphes" (Paris: Gauthier-Villar 1929) and "Eindeutige analytische Funktionen" (Die Grundlehren dt mathematischen Wissenschaften in Einzeldarstellungen, VoL 46, 1: edition Berlin: Springer 1936, 2nd edition Berlin-Gottingen-Heidelberg Springer 1953). In these presentations I have strived to make the individual result and their proofs readily understandable and to treat them in the ligh of certain guiding principles in a unified way. A decisive step in thi direction within the theory of entire and meromorphic functions consiste- in replacing the classical representation of these functions through ca nonical products with more general tools from the potential theor (Green's formula and especially the Poisson-Jensen formula). On thi foundation it was possible to introduce the quantities (the characteristic the proximity and the counting functions) which are definitive for th

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