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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.
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.
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Part 1. The work of T. KawaiPublications of Professor Takahiro KawaiThe work of T. Kawai on hyperfunction theory and microlocal analysis, Part 1 -- Microlocal analysis and differential equations by Nobuyuki ToseThe work of T. Kawai on hyperfunction theory and microlocal analysis, Part 2 -- Operators of infinite order and convolution equations by Takashi AokiThe work of T. Kawai on exact WKB analysis by Yoshitsugu Takei Part 2. Contributed papersVirtual 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 TakeiRegular sequences associated with the Noumi-Yamada equations with a large parameter by Takashi Aoki, Naofumi HondaGhost busting: Making sense of non-Hermitian Hamiltonians by Carl M. BenderVanishing of the logarithmic trace of generalized Szego projectors by Louis Boutet de MonvelNonlinear Stokes phenomena in first or second order differential equations by Ovidiu CostinReconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation by Yuki Daido, Hyeonbae Kang, Gen NakamuraExact WKB analysis near a simple turning point by Eric DelabaereThe Borel transform by Leon EhrenpreisOn the use of Z-transforms in the summation of transseries for partial differential equations by Christopher J. HowlsSome dynamical aspects of Painleve VI by Katsunori IwasakiAn algebraic representation for correlation functions in integrable spin chains by Michio JimboInverse image of D-modules and quasi-b-functions by Yves LaurentThe hypoelliptic Laplacian of J.-M. Bismut by Gilles LebeauCommuting differential operators with regular siongularities by Toshio OshimaThe behaviors of singular solutions of some partial differential equations in the complex domain by Sunao OuchiObservations on the JWKB treatment of the quadratic barrier by Hujun Shen, Harris J. SilverstoneA role of virtual turning points and new Stokes curves in Stokes geometry of the quantum Henon map by Akira ShudoSpectral instability for non-selfadjoint operators by Johannes SjostrandBondary and lens rigidity, tensor tomography and analytic microlocal analysis by Plamen Stefanov, Gunther UhlmannCoupling of two partial differential equations and its application by Hidetoshi TaharaInstanton-type formal solutions for the first Painleve hierarchy by Yoshitsugu TakeiFrom exact-WKB toward singular quantum perturbation theory II by Andre VorosWKB analysis and Poincare theorem for vector fields by Masafumi Yoshino
Part 1. The work of T. KawaiPublications of Professor Takahiro KawaiThe work of T. Kawai on hyperfunction theory and microlocal analysis, Part 1 -- Microlocal analysis and differential equations by Nobuyuki ToseThe work of T. Kawai on hyperfunction theory and microlocal analysis, Part 2 -- Operators of infinite order and convolution equations by Takashi AokiThe work of T. Kawai on exact WKB analysis by Yoshitsugu Takei Part 2. Contributed papersVirtual 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 TakeiRegular sequences associated with the Noumi-Yamada equations with a large parameter by Takashi Aoki, Naofumi HondaGhost busting: Making sense of non-Hermitian Hamiltonians by Carl M. BenderVanishing of the logarithmic trace of generalized Szego projectors by Louis Boutet de MonvelNonlinear Stokes phenomena in first or second order differential equations by Ovidiu CostinReconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation by Yuki Daido, Hyeonbae Kang, Gen NakamuraExact WKB analysis near a simple turning point by Eric DelabaereThe Borel transform by Leon EhrenpreisOn the use of Z-transforms in the summation of transseries for partial differential equations by Christopher J. HowlsSome dynamical aspects of Painleve VI by Katsunori IwasakiAn algebraic representation for correlation functions in integrable spin chains by Michio JimboInverse image of D-modules and quasi-b-functions by Yves LaurentThe hypoelliptic Laplacian of J.-M. Bismut by Gilles LebeauCommuting differential operators with regular siongularities by Toshio OshimaThe behaviors of singular solutions of some partial differential equations in the complex domain by Sunao OuchiObservations on the JWKB treatment of the quadratic barrier by Hujun Shen, Harris J. SilverstoneA role of virtual turning points and new Stokes curves in Stokes geometry of the quantum Henon map by Akira ShudoSpectral instability for non-selfadjoint operators by Johannes SjostrandBondary and lens rigidity, tensor tomography and analytic microlocal analysis by Plamen Stefanov, Gunther UhlmannCoupling of two partial differential equations and its application by Hidetoshi TaharaInstanton-type formal solutions for the first Painleve hierarchy by Yoshitsugu TakeiFrom exact-WKB toward singular quantum perturbation theory II by Andre VorosWKB analysis and Poincare theorem for vector fields by Masafumi Yoshino
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