Takahiro Kawai

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Takahiro Kawai

Takahiro Kawai ( Japanese 河 合 隆裕 , Kawai Takahiro ; * 1945 in Tsushima ) is a Japanese mathematician who deals with micro-local analysis . He is Professor at the Research Institute for Mathematical Sciences (RIMS) at Kyōto University .

Life

Kawai is a student of Mikio Satō at the University of Tokyo and was with Masaki Kashiwara after 1968 an essential collaborator of Satō in the elaboration of his theories on micro-local analysis (called algebraic analysis in the Sato school). He was Satō's assistant at RIMS, received his doctorate from Satō in 1973 in Kyoto ( On the global existence of real analytic solutions of linear differential equations ) and later professor there.

In 1977/78 he was at the Institute for Advanced Study in Princeton and organized a seminar on micro-local analysis with Kashiwara.

He studied the micro-local analysis of linear differential equations and S-matrices in quantum field theory (including infrared singularities) and the exact WKB approximation of solutions to linear and nonlinear differential equations. Together with T. Aoki and Y. Takei, he investigated the singularities of the Borel transformation of WKB solutions in the context of microlocal analysis and introduced the concept of the virtual turning point.

In 1977 he received the Iyanaga Prize of the Japanese Mathematical Society ,

Fonts

  • with Sato, Kashiwara: Microfunctions and pseudodifferential equations. In: Komatsu (Ed.): Hyperfunctions and pseudodifferential equations. Proceedings Katata 1971, Springer-Verlag, Lecture Notes in Mathematics Vol. 287, 1973, pp. 265-529.
  • with Kashiwara, Tatsuo Kimura: Foundations of algebraic analysis , Princeton 1986
  • Microlocal analysis and asymptotic analysis , Kyoto: RIMS 2004
  • Editor with Keiko Fujita: Microlocal analysis and complex Fourier analysis , World Scientific 2002
  • with Victor Guillemin , Kashiwara: Seminar on micro-local analysis , Annals of Mathematical Studies, Princeton University Press 1979
  • with Kashiwara, Henry Stapp: Micro-analyticity of the S-matrix and related functions , Comm. Math. Phys., Vol. 66, 1979, pp. 95-130, Project Euclid
  • with T. Aoki, Y. Takei: The Bender-Wu analysis and the Voros theory . Proc. Special Functions, Springer, 1991, pp. 1-29, Part 2 in Advanced Studies in Pure Mathematics 54, Mathematical Society of Japan, Tokyo 2009, pp. 19-94
  • with Aoki, Takei: On the exact steepest descent method: a new method for the description of Stokes curves , J. Math. Phys. 42, 2001, 3691-3713
  • with Aoki, Takei: New turning points in the exact WKB-analysis of higher order differential equations , in: Analyze algèbrique des perturbations singulières I, Paris: Hermann 1994, pp. 69-84
  • with Aoki, Takei, T. Koike: On the exact WKB-analysis of operators admitting infinitely many phases , Adv. Math. 181, 2004, 165-189
  • with Aoki, Takei, S. Sasaki, A. Shudo: Virtual turning points and bifurcation of Stokes curves , J. Phys. A, 38, 2005, 3317-3336

literature

  • Takashi Aoki (Ed.), Algebraic analysis of differential equations: From microlocal analysis to exponential asymptotics. Festschrift in honor of Takahiro Kawai, Springer 2007

Web links

Individual evidence

  1. ↑ IAS Membership Book 1980
  2. ↑ Mikio Sato, McTutor
  3. ↑ Entry 000008591813 in the Doctoral Dissertation Bibliographic Database of the National Institute of Informatics
  4. ↑ Takahiro Kawai: On the global existence of real analytic solutions of linear differential equations, I . In: Proceedings of the Japan Academy . Vol. 47, No. 6 , 1971, p. 537-540 , doi : 10.3792 / pja / 1195519901 (full text).
  5. ↑ Takahiro Kawai: On the global existence of real analytic solutions of linear differential equations, II . In: Proceedings of the Japan Academy . Vol. 47, Number 7, Supplement, 1971, pp. 643-647 , doi : 10.3792 / pja / 1195526433 (full text).
personal data
SURNAME Kawai, Takahiro
ALTERNATIVE NAMES 河 合 隆裕 (Japanese)
BRIEF DESCRIPTION Japanese mathematician
DATE OF BIRTH 1945
PLACE OF BIRTH Tsushima (Aichi)