Preface. Naofumi Honda Yasunori Okada Susumu Yamazaki
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1 Preface This volume presents a collection of research and survey articles which were contributed by invited speakers in the RIMS workshop Several aspects of microlocal analysis held at Research Institute for Mathematical Sciences (RIMS), Kyoto University from 20 through 24 October, 2014, in which experts from many areas of mathematics participated. Naofumi Honda Yasunori Okada Susumu Yamazaki i
2 ii Program RIMS Workshop on Several aspects of microlocal analysis Organizers: Naofumi Honda (Hokkaido Univ.), Yasunori Okada (Chiba Univ.) and Susumu Yamazaki (Nihon Univ.) October 20 (Mon.) 24 (Fri.), 2014, October 20, Monday Room No.111 of RIMS, Kyoto University 10:00-10:50 Shinya Moritoh (Nara Women s Univ.) Detection of singularities in wavelet and ridgelet analyses 11:10-12:00 Hideshi Yamane (Kwansei Gakuin Univ.) Asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation 13:40-14:30 Akira Shudo (Tokyo Metropolitan Univ.) Quantum tunneling in nonintegrable systems: beyond the leading order WKB description 14:50-15:40 Sampei Hirose (Shibaura Institute of Technology) On unfoldings of differential operators 16:00-16:50 Takashi Aoki (Kindai Univ.) The hypergeometric function and WKB solutions October 21, Tuesday 10:00-10:50 Yasunori Okada (Chiba Univ.) Solvability of coupling equations and infinite dimensional holomorphy 11:10-12:00 Toshinori Oaku (Tokyo Woman s Christian Univ.) Annihilators of Laurent coefficients of the complex power of a real analytic function example and algorithm 13:40-14:30 Kunio Yoshino (Tokyo City Univ.) Spectral analysis of Toeplitz operators on Bargmann - Fock space via hyperfunctions 14:50-15:40 Kohei Umeta (Hokkaido Univ.) and Naofumi Honda (Hokkaido Univ.) On the construction of Laplace transforms for Laplace hyperfunctions 16:00-16:50 Hidetoshi Tahara (Sophia Univ.) q-analogues of Laplace and Borel transforms by using q-exponentials
3 iii October 22, Wednesday 10:00-10:50 Luca Prelli (Univ. Lisbon), Naofumi Honda (Hokkaido Univ.) and Susumu Yamazaki (Nihon Univ.) Multi-microlocalization 11:10-12:00 Keisuke Uchikoshi (National Defense Academy of Japan) Singularities in a compressible perfect fluid 13:40-14:30 Yoko Umeta (Tokyo Univ. of Science) and Shinichi Tajima (Tsukuba Univ.) On the monodromy structure of holonomic D-modules associated with simple line singularities 14:50-15:40 Joe Kamimoto (Kyushu Univ.) On local zeta functions in two dimensions 16:00-16:50 Kiyoomi Kataoka (Univ. Tokyo) A review of the results on second analytic singularities in diffraction problems, and some geometric proofs October 23, Thursday 10:00-10:50 Susumu Yamazaki (Nihon Univ.) Boundary value problem for hyperfunction solutions to Fuchsian systems 11:10-12:00 Takashi Takiguchi (National Defense Academy of Japan) On uniqueness problems for the Radon transform 13:40-14:30 Naofumi Honda (Hokkaido Univ.) and Takahiro Kawai (RIMS) A study of pinch points and cups in the Landau-Nakanishi geometry 14:50-15:40 Tatsuya Koike (Kobe Univ.) On Voros coefficients and middle convolutions for linear ordinary differential equations with a large parameter 16:00-16:50 David Sauzin (French National Center for Scientific Research) Nonlinear analysis with resurgent functions, I
4 iv October 24, Friday 10:00-10:50 David Sauzin (French National Center for Scientific Research) Nonlinear analysis with resurgent functions, II 11:10-12:00 Shingo Kamimoto (RIMS), Takahiro Kawai (RIMS) and Tatsuya Koike (Kobe Univ.) Exact WKB analysis of simple pole type operators alien calculus using the differential operators of infinite order 13:40-14:30 Hidekazu Ito (Kanazawa Univ.) Some aspects of integrability of vector fields and normal form theory 14:50-15:40 Kohei Iwaki (RIMS) Exact WKB analysis and cluster algebras 16:00-16:50 Masafumi Yoshino (Hiroshima Univ.) Monodromy of confluent hypergeometric system
5 v Contents Preface... Program... i ii Articles 1. Shinya Moritoh, Detection of singularities in wavelet and ridgelet analyses Hideshi Yamane, Asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation Akira Shudo, Yasutaka Hanada and Kensuke S. Ikeda, Quantum tunneling in nonintegrable systems: beyond the leading order semiclassical description Sampei Hirose, On the redundant and non-redundant virtual turning points for the AKT equation Takashi Aoki, Toshinori Takahashi and Mika Tanda, The hypergeometric function and WKB solutions Yasunori Okada, Reinhard Schäfke and Hidetoshi Tahara, Unique solvability of coupling equations in holomorphic functions Toshinori Oaku, Annihilators of Laurent coefficients of the complex power for normal crossing singularity Kohei Umeta, A Laplace transform of Laplace hyperfunctions in several variables Naofumi Honda, Luca Prelli and Susumu Yamazaki, Multimicrolocalization Keisuke Uchikoshi, Singularities in a compressible perfect fluid Shinichi Tajima and Yoko Umeta, Computing structures of holonomic D-modules associated with a simple line singularity Joe Kamimoto and Toshihiro Nose, On the asymptotic expansion of oscillatory integrals with smooth phases in two dimensions Kiyoomi Kataoka, A review of the results on second analytic singularities in diffraction problems Susumu Yamazaki, Boundary value problem for Hyperfunction solutions to Fuchsian systems Naofumi Honda and Takahiro Kawai, A study of pinch points and cusps in the Landau-Nakanishi geometry Shingo Kamimoto and David Sauzin, Nonlinear analysis with endlessly continuable functions
6 vi 17. Hidekazu Ito, Some remarks on integrability and normal forms for vector fields Kohei Iwaki, Exact WKB analysis, cluster algebras and Fock-Goncharov coordinates Masafumi Yoshino, Monodromy of confluent hypergeometric system of Okubo type
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