Analytic, Algebraic and Geometric Aspects of Differential Equations : Będlewo, Poland, September 2015
 フォーマット:
 電子ブック
 責任表示:
 edited by Galina Filipuk, Yoshishige Haraoka, Sławomir Michalik
 本文言語:
 英語
 出版情報:
 Cham, Germany. 2017. Springer International Publishing,Imprint: Birkhäuser
 シリーズ:
 Trends in Mathematics
 概要:
 This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for nonspecialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, earlycareer researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques. … 続きを見る
 目次:

Preface An introduction to Dunkl theory and its analytic aspects Holonomic Systems SubRiemannian geometry and hypoelliptic operators Asymptotic analysis and summability of formal power series WKB analysis and Stokes geometry of differential equations Transcendental Meromorphic Solutions of P34 and Small Targets Towards the convergence of generalized power series solutions of algebraic ODEs Connection problem for regular holonomic systems in several variables On ksummability of formal solutions for certain higher order partial differential operators with polynomial coefficients On Stokes phenomena for the alternate discrete PI equation Flat structures and algebraic solutions to Painlevé VI equation Relation of Semiclassical orthogonal polynomials to General Schlesinger systems via Twistor theory Some notes on the multilevel Gevrey solutions of singularly perturbed linear partial differential equations Reducibility of hypergeometric equations Parametric Borel summability of partial differential equations of irregular singular type. Preface An introduction to Dunkl theory and its analytic aspects Holonomic Systems SubRiemannian geometry and hypoelliptic operators Asymptotic analysis and summability of formal power series WKB analysis and Stokes geometry of differential equations
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