Algebraic Analysis of Differential Equations [electronic resource] : from Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai / edited by Takashi Aoki, Hideyuki Majima, Yoshitsugu Takei, Nobuyuki Tose.

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.