Algebraic Analysis of Differential Equations: From Microlocal Analysis to Exponential Asymptotics

ISBN-13: 9784431998273 / Angielski / Miękka / 2010 / 354 str.

T. Aoki; H. Majima; Y. Takei

Opis

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."

Spis treści

Part 1. The work of T. Kawai Publications of Professor Takahiro Kawai The work of T. Kawai on hyperfunction theory and microlocal analysis, Part 1 -- Microlocal analysis and differential equations by Nobuyuki Tose The work of T. Kawai on hyperfunction theory and microlocal analysis, Part 2 -- Operators of infinite order and convolution equations by Takashi Aoki The work of T. Kawai on exact WKB analysis by Yoshitsugu Takei Part 2. Contributed papers Virtual turning points -- A gift of microlocal analysis to the exact WKB analysis by Takashi Aoki, Naofumi Honda, Takahiro Kawai, Tatsuya Koike, Yukihiro Nishikawa, Shunsuke Sasaki, Akira Shudo, Yoshitsugu Takei Regular sequences associated with the Noumi-Yamada equations with a large parameter by Takashi Aoki, Naofumi Honda Ghost busting: Making sense of non-Hermitian Hamiltonians by Carl M. Bender Vanishing of the logarithmic trace of generalized Szego projectors by Louis Boutet de Monvel Nonlinear Stokes phenomena in first or second order differential equations by Ovidiu Costin Reconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation by Yuki Daido, Hyeonbae Kang, Gen Nakamura Exact WKB analysis near a simple turning point by Eric Delabaere The Borel transform by Leon Ehrenpreis On the use of Z-transforms in the summation of transseries for partial differential equations by Christopher J. Howls Some dynamical aspects of Painleve VI by Katsunori Iwasaki An algebraic representation for correlation functions in integrable spin chains by Michio Jimbo Inverse image of D-modules and quasi-b-functions by Yves Laurent The hypoelliptic Laplacian of J.-M. Bismut by Gilles Lebeau Commuting differential operators with regular siongularities by Toshio Oshima The behaviors of singular solutions of some partial differential equations in the complex domain by Sunao Ouchi Observations on the JWKB treatment of the quadratic barrier by Hujun Shen, Harris J. Silverstone A role of virtual turning points and new Stokes curves in Stokes geometry of the quantum Henon map by Akira Shudo Spectral instability for non-selfadjoint operators by Johannes Sjostrand Bondary and lens rigidity, tensor tomography and analytic microlocal analysis by Plamen Stefanov, Gunther Uhlmann Coupling of two partial differential equations and its application by Hidetoshi Tahara Instanton-type formal solutions for the first Painleve hierarchy by Yoshitsugu Takei From exact-WKB toward singular quantum perturbation theory II by Andre Voros WKB analysis and Poincare theorem for vector fields by Masafumi Yoshino