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.

Contenu
The work of T. Kawai.- Publications of Professor Takahiro Kawai.- The work of T. Kawai on hyperfunction theory and microlocal analysis.- The work of T. Kawai on hyperfunction theory and microlocal analysis.- The work of T. Kawai on exact WKB analysis.- Contributed papers.- Virtual turning points A gift of microlocal analysis to the exact WKB analysis.- Regular sequences associated with the Noumi-Yamada equations with a large parameter.- Ghost busting: Making sense of non-Hermitian Hamiltonians.- Vanishing of the logarithmic trace of generalized Szegö projectors.- Nonlinear Stokes phenomena in first or second order differential equations.- Reconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation.- Exact WKB analysis near a simple turning point.- The Borel transform.- On the use of Z-transforms in the summation of transseries for partial differential equations.- Some dynamical aspects of Painlevé VI.- An algebraic representation for correlation functions in integrable spin chains.- Inverse image of D-modules and quasi-b-functions.- The hypoelliptic Laplacian of J.-M. Bismut.- Commuting differential operators with regular singularities.- The behaviors of singular solutions of some partial differential equations in the complex domain.- Observations on the JWKB treatment of the quadratic barrier.- A role of virtual turning points and new Stokes curves in Stokes geometry of the quantum Hénon map.- Spectral instability for non-selfadjoint operators.- Boundary and lens rigidity, tensor tomography and analytic microlocal analysis.- Coupling of two partial differential equations and its application.- Instanton-type formal solutions for the first Painlevé hierarchy.- From exact-WKB toward singular quantum perturbation theory II.-WKB analysis and Poincaré theorem for vector fields.