Algebraic Analysis of Differential Equations

Table of Contents

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   Book Overview
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   Chapter 1 Publications of Professor Takahiro Kawai
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   Chapter 2 The work of T. Kawai on hyperfunction theory and microlocal analysis
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   Chapter 3 The work of T. Kawai on hyperfunction theory and microlocal analysis
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   Chapter 4 The work of T. Kawai on exact WKB analysis
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   Chapter 5 Virtual turning points — A gift of microlocal analysis to the exact WKB analysis
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   Chapter 6 Regular sequences associated with the Noumi-Yamada equations with a large parameter
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   Chapter 7 Ghost busting: Making sense of non-Hermitian Hamiltonians
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   Chapter 8 Vanishing of the logarithmic trace of generalized Szegö projectors
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    Chapter 9 Nonlinear Stokes phenomena in first or second order differential equations
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    Chapter 10 Reconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation
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    Chapter 11 Exact WKB analysis near a simple turning point
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    Chapter 12 The Borel transform
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    Chapter 13 On the use of Z-transforms in the summation of transseries for partial differential equations
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    Chapter 14 Some dynamical aspects of Painlevé VI
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    Chapter 15 An algebraic representation for correlation functions in integrable spin chains
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    Chapter 16 Inverse image of D-modules and quasi- b -functions
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    Chapter 17 The hypoelliptic Laplacian of J.-M. Bismut
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    Chapter 18 Commuting differential operators with regular singularities
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    Chapter 19 The behaviors of singular solutions of some partial differential equations in the complex domain
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    Chapter 20 Observations on the JWKB treatment of the quadratic barrier
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    Chapter 21 A role of virtual turning points and new Stokes curves in Stokes geometry of the quantum Hénon map
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    Chapter 22 Spectral instability for non-selfadjoint operators
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    Chapter 23 Boundary and lens rigidity, tensor tomography and analytic microlocal analysis
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    Chapter 24 Coupling of two partial differential equations and its application
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    Chapter 25 Instanton-type formal solutions for the first Painlevé hierarchy
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    Chapter 26 From exact-WKB toward singular quantum perturbation theory II
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    Chapter 27 WKB analysis and Poincaré theorem for vector fields