From Divergent Power Series To Analytic Functions
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| Author | : Werner Balser |
| Publisher | : Springer |
| Total Pages | : 117 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540485945 |
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.
| Author | : Werner Balser |
| Publisher | : |
| Total Pages | : 124 |
| Release | : 2014-01-15 |
| Genre | : |
| ISBN | : 9783662187739 |
| Author | : Galina Filipuk |
| Publisher | : Springer |
| Total Pages | : 273 |
| Release | : 2018-09-24 |
| Genre | : Mathematics |
| ISBN | : 3319991485 |
These proceedings provide methods, techniques, different mathematical tools and recent results in the study of formal and analytic solutions to Diff. (differential, partial differential, difference, q-difference, q-difference-differential.... ) Equations. They consist of selected contributions from the conference "Formal and Analytic Solutions of Diff. Equations", held at Alcalá de Henares, Spain during September 4-8, 2017. Their topics include summability and asymptotic study of both ordinary and partial differential equations. The volume is divided into four parts. The first paper is a survey of the elements of nonlinear analysis. It describes the algorithms to obtain asymptotic expansion of solutions of nonlinear algebraic, ordinary differential, partial differential equations, and of systems of such equations. Five works on formal and analytic solutions of PDEs are followed by five papers on the study of solutions of ODEs. The proceedings conclude with five works on related topics, generalizations and applications. All contributions have been peer reviewed by anonymous referees chosen among the experts on the subject. The volume will be of interest to graduate students and researchers in theoretical and applied mathematics, physics and engineering seeking an overview of the recent trends in the theory of formal and analytic solutions of functional (differential, partial differential, difference, q-difference, q-difference-differential) equations in the complex domain.
| Author | : Martin Fuchs |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 284 |
| Release | : 2000-12-12 |
| Genre | : Mathematics |
| ISBN | : 9783540413974 |
Variational methods are applied to prove the existence of weak solutions for boundary value problems from the deformation theory of plasticity as well as for the slow, steady state flow of generalized Newtonian fluids including the Bingham and Prandtl-Eyring model. For perfect plasticity the role of the stress tensor is emphasized by studying the dual variational problem in appropriate function spaces. The main results describe the analytic properties of weak solutions, e.g. differentiability of velocity fields and continuity of stresses. The monograph addresses researchers and graduate students interested in applications of variational and PDE methods in the mechanics of solids and fluids.
| Author | : Nigel J. Cutland |
| Publisher | : Springer |
| Total Pages | : 118 |
| Release | : 2004-10-11 |
| Genre | : Mathematics |
| ISBN | : 3540445315 |
This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed.
| Author | : Lars Wahlbin |
| Publisher | : Springer |
| Total Pages | : 179 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540494014 |
This book is essentially a set of lecture notes from a graduate seminar given at Cornell in Spring 1994. It treats basic mathematical theory for superconvergence in the context of second order elliptic problems. It is aimed at graduate students and researchers. The necessary technical tools are developed in the text although sometimes long proofs are merely referenced. The book gives a rather complete overview of the field of superconvergence (in time-independent problems). It is the first text with such a scope. It includes a very complete and up-to-date list of references.
| Author | : Galina Filipuk |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 520 |
| Release | : 2019-11-18 |
| Genre | : Mathematics |
| ISBN | : 3110609614 |
With a balanced combination of longer survey articles and shorter, peer-reviewed research-level presentations on the topic of differential and difference equations on the complex domain, this edited volume presents an up-to-date overview of areas such as WKB analysis, summability, resurgence, formal solutions, integrability, and several algebraic aspects of differential and difference equations.
| Author | : Max Koecher |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 198 |
| Release | : 1999-09-17 |
| Genre | : Mathematics |
| ISBN | : 9783540663607 |
This volume contains a re-edition of Max Koecher's famous Minnesota Notes. The main objects are homogeneous, but not necessarily convex, cones. They are described in terms of Jordan algebras. The central point is a correspondence between semisimple real Jordan algebras and so-called omega-domains. This leads to a construction of half-spaces which give an essential part of all bounded symmetric domains. The theory is presented in a concise manner, with only elementary prerequisites. The editors have added notes on each chapter containing an account of the relevant developments of the theory since these notes were first written.
| Author | : David Mumford |
| Publisher | : Springer |
| Total Pages | : 316 |
| Release | : 2004-02-21 |
| Genre | : Mathematics |
| ISBN | : 3540460217 |
Mumford's famous "Red Book" gives a simple, readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduates or mathematicians in other fields wishing to quickly learn aboutalgebraic geometry. This new edition includes an appendix that gives an overview of the theory of curves, their moduli spaces and their Jacobians -- one of the most exciting fields within algebraic geometry.
| Author | : Igor Nikolaev |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 324 |
| Release | : 1999-07-15 |
| Genre | : Mathematics |
| ISBN | : 9783540660804 |
Time-evolution in low-dimensional topological spaces is a subject of puzzling vitality. This book is a state-of-the-art account, covering classical and new results. The volume comprises Poincaré-Bendixson, local and Morse-Smale theories, as well as a carefully written chapter on the invariants of surface flows. Of particular interest are chapters on the Anosov-Weil problem, C*-algebras and non-compact surfaces. The book invites graduate students and non-specialists to a fascinating realm of research. It is a valuable source of reference to the specialists.
