T. Aoki & H. Majima 
Algebraic Analysis of Differential Equations [PDF ebook] 
from Microlocal Analysis to Exponential Asymptotics

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.