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Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation
These are the proceedings of a one-week international conference centered on asymptotic analysis and its applications. They contain major contributions dealing with: mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis, local dynamics: parabolic systems, small denominator questions, new aspects in mould calculus, with related combinatorial Hopf algebras and application to multizeta values, a new family of resurgent functions related to knot theory.
Algebraic Analysis of Differential Equations
This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the conference "Algebraic Analysis of Differential Equations – from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. This volume is dedicated to Professor Takahiro Kawai, who is one of the creators of microlocal analysis and who introduced the technique of microlocal analysis into exponential asymptotics.
Differential Equations And The Stokes Phenomenon
This volume is the record of a workshop on differential equations and the Stokes phenomenon, held in May 2001 at the University of Groningen. It contains expanded versions of most of the lectures given at the workshop. To a large extent, both the workshop and the book may be regarded as a sequel to a conference held in Groningen in 1995 which resulted in the book The Stokes Phenomenon and Hilbert's 16th Problem (B L J Braaksma, G K Immink and M van der Put, editors), also published by World Scientific (1996).Both books offer a snapshot concerning the state of the art in the areas of differential, difference and q-difference equations. Apart from the asymptotics of solutions, Painlevé properties and the algebraic theory, new topics addressed in the second book include arithmetic theory of linear equations, and Galois theory and Lie symmetries of nonlinear differential equations.
The Philosophy of Cosmology
This book addresses foundational questions raised by observational and theoretical progress in modern cosmology. As the foundational volume of an emerging academic discipline, experts from relevant fields lay out the fundamental problems of contemporary cosmology and explore the routes toward finding possible solutions, for a broad academic audience.
A Vector Field Method on the Distorted Fourier Side and Decay for Wave Equations with Potentials
The authors study the Cauchy problem for the one-dimensional wave equation ∂2tu(t,x)−∂2xu(t,x)+V(x)u(t,x)=0. The potential V is assumed to be smooth with asymptotic behavior V(x)∼−14|x|−2 as |x|→∞. They derive dispersive estimates, energy estimates, and estimates involving the scaling vector field t∂t+x∂x, where the latter are obtained by employing a vector field method on the “distorted” Fourier side. In addition, they prove local energy decay estimates. Their results have immediate applications in the context of geometric evolution problems. The theory developed in this paper is fundamental for the proof of the co-dimension 1 stability of the catenoid under the vanishing mean curvature flow in Minkowski space; see Donninger, Krieger, Szeftel, and Wong, “Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space”, preprint arXiv:1310.5606 (2013).
Theory of Fundamental Bessel Functions of High Rank
In this article, the author studies fundamental Bessel functions for $mathrm{GL}_n(mathbb F)$ arising from the Voronoí summation formula for any rank $n$ and field $mathbb F = mathbb R$ or $mathbb C$, with focus on developing their analytic and asymptotic theory. The main implements and subjects of this study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. The author proves the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.
Semi-bounded Differential Operators, Contractive Semigroups and Beyond
In the present book the conditions are studied for the semi-boundedness of partial differential operators which is interpreted in different ways. Nowadays one knows rather much about L2-semibounded differential and pseudo-differential operators, although their complete characterization in analytic terms causes difficulties even for rather simple operators. Until recently almost nothing was known about analytic characterizations of semi-boundedness for differential operators in other Hilbert function spaces and in Banach function spaces. The goal of the present book is to partially fill this gap. Various types of semi-boundedness are considered and some relevant conditions which are either necessary and sufficient or best possible in a certain sense are given. Most of the results reported in this book are due to the authors.
Mathematical Methods Of Theoretical Physics
'This book could serve either as a good reference to remind students about what they have seen in their completed courses or as a starting point to show what needs more investigation. Svozil (Vienna Univ. of Technology) offers a very thorough text that leaves no mathematical area out, but it is best described as giving a synopsis of each application and how it relates to other areas … The text is organized well and provides a good reference list. Summing Up: Recommended. Upper-division undergraduates and graduate students.'CHOICEThis book contains very explicit proofs and demonstrations through examples for a comprehensive introduction to the mathematical methods of theoretical physics. It also combines and unifies many expositions of this subject, suitable for readers with interest in experimental and applied physics.
Asymptotics and Borel Summability
Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, tr
