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 | : Wolfgang Arendt |
| Publisher | : John Wiley & Sons |
| Total Pages | : 502 |
| Release | : 2009-07-10 |
| Genre | : Science |
| ISBN | : 3527628037 |
Mathematical Analysis of Evolution, Information, and Complexity deals with the analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in science, this text covers a broad range of problems including diffusion processes, neuronal networks, quantum theory and cosmology. Bringing together a wide collection of research in mathematics, information theory, physics and other scientific and technical areas, this new title offers elementary and thus easily accessible introductions to the various fields of research addressed in the book.
| Author | : Po-Fang Hsieh |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 480 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461215064 |
Providing readers with the very basic knowledge necessary to begin research on differential equations with professional ability, the selection of topics here covers the methods and results that are applicable in a variety of different fields. The book is divided into four parts. The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness. The second part describes the basic results concerning linear differential equations, while the third deals with nonlinear equations. In the last part the authors write about the basic results concerning power series solutions. Each chapter begins with a brief discussion of its contents and history, and hints and comments for many problems are given throughout. With 114 illustrations and 206 exercises, the book is suitable for a one-year graduate course, as well as a reference book for research mathematicians.
| Author | : J. Bertoin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 308 |
| Release | : 1999-11-17 |
| Genre | : Mathematics |
| ISBN | : 9783540665939 |
Lecture Notes in Mathematics This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. The type of material considered for publication includes 1. Research monographs 2. Lectures on a new field or presentations of a new angle in a classical field 3. Summer schools and intensive courses on topics of current research Texts which are out of print but still in demand may also be considered. The timeliness of a manuscript is sometimes more important than its form, which might be preliminary or tentative. Details of the editorial policy can be found on the inside front-cover of a current volume. Manuscripts should be submitted in camera-ready form according to Springer-Verlag's specification: technical instructions will be sent on request. TEX macros may be found at: http://www.springer.de/math/authors/b-tex.html Select the version of TEX you use and then click on "Monographs". A subject index should be included. We recommend contacting the publisher or the series editors at an early stage of your project. Addresses are given on the inside back-cover.
| Author | : J. Coates |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 276 |
| Release | : 1999-10-19 |
| Genre | : Mathematics |
| ISBN | : 9783540665465 |
This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. instructional conference held in Cetraro, Italy, from July 12 to 19, 1997. The papers collected here are broad surveys of the current research in the arithmetic of elliptic curves, and also contain several new results which cannot be found elsewhere in the literature. Owing to clarity and elegance of exposition, and to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians.
| Author | : Paul A. Meyer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 330 |
| Release | : 1995-11-17 |
| Genre | : Mathematics |
| ISBN | : 9783540602705 |
In recent years, the classical theory of stochastic integration and stochastic differential equations has been extended to a non-commutative set-up to develop models for quantum noises. The author, a specialist of classical stochastic calculus and martingale theory, tries to provide an introduction to this rapidly expanding field in a way which should be accessible to probabilists familiar with the Ito integral. It can also, on the other hand, provide a means of access to the methods of stochastic calculus for physicists familiar with Fock space analysis. For this second edition, the author has added about 30 pages of new material, mostly on quantum stochastic integrals.
| Author | : Frederic Fauvet |
| Publisher | : Walter de Gruyter |
| Total Pages | : 257 |
| Release | : 2008-08-22 |
| Genre | : Mathematics |
| ISBN | : 3110200007 |
This volume contains nine refereed research papers in various areas from combinatorics to dynamical systems, with computer algebra as an underlying and unifying theme. Topics covered include irregular connections, rank reduction and summability of solutions of differential systems, asymptotic behaviour of divergent series, integrability of Hamiltonian systems, multiple zeta values, quasi-polynomial formalism, Padé approximants related to analytic integrability, hybrid systems. The interactions between computer algebra, dynamical systems and combinatorics discussed in this volume should be useful for both mathematicians and theoretical physicists who are interested in effective computation.
| Author | : Marius van der Put |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 446 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642557503 |
From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews
