Analytic, Algebraic and Geometric Aspects of Differential Equations (eBook)

Będlewo, Poland, September 2015

Galina Filipuk, Yoshishige Haraoka, Sławomir Michalik (Herausgeber)

eBook Download: PDF

2017 | 1st ed. 2017
VIII, 471 Seiten
Springer International Publishing (Verlag)
978-3-319-52842-7 (ISBN)

Infos

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 non-specialists), 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, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.

Inhalt

Preface.- An introduction to Dunkl theory and its analytic aspects.- Holonomic Systems.- Sub-Riemannian geometry and hypoelliptic operators.- Asymptotic analysis and summability of formal power series.- WKB analysis and Stokes geometry of differential equations.- Transcendental Meromorphic Solutions of P34and Small Targets.- Towards the convergence of generalized power series solutions of algebraic ODEs.- Connection problem for regular holonomic systems in several variables.- On k-summability 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 toPainlevé VI equation.- Relation of Semi-classical orthogonal polynomials to General Schlesinger systems via Twistor theory.- Some notes on the multi-level Gevrey solutions of singularly perturbed linear partial differential equations.- Reducibility of hypergeometric equations.- Parametric Borel summability of partial differential equations of irregular singular type.

Produkt-Details

• Erscheint lt. Verlag: 23.6.2017
• Reihe/Serie: Trends in Mathematics
• Reihe/Serie: Trends in Mathematics
• Zusatzinfo: VIII, 471 p. 32 illus., 14 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Schlagworte: asymptotic expansions • Dunkl theory, special functions • formal solutions of PDEs • Gevrey estimates • holomorphic vector fields, normal forms • holonomic systems • integrable systems with applications to mathematical physics • ODEs in the complex plane • Ordinary differential equations • Partial differential equations • sub-Riemannian geometry and sub-elliptic operators • summability of formal solutions of difference equations • WKB analysis and Stokes geometry of differential equations
• ISBN-10: 3-319-52842-4 / 3319528424
• ISBN-13: 978-3-319-52842-7 / 9783319528427