Aoki, Takashi

Algebraic Analysis of Differential Equations

Aoki, Takashi - Algebraic Analysis of Differential Equations, ebook


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Table of contents

Part I. The work of T. Kawai

1. Publications of Professor Takahiro Kawai

2. The work of T. Kawai on hyperfunction theory and microlocal analysis
Nobuyuki Tose

3. The work of T. Kawai on hyperfunction theory and microlocal analysis
Takashi Aoki

4. The work of T. Kawai on exact WKB analysis
Yoshitsugu Takei

Part II. Contributed papers

5. Virtual turning points — A gift of microlocal analysis to the exact WKB analysis
Takashi Aoki, Naofumi Honda, Takahiro Kawai, Tatsuya Koike, Yukihiro Nishikawa, Shunsuke Sasaki, Akira Shudo, Yoshitsugu Takei

6. Regular sequences associated with the Noumi-Yamada equations with a large parameter
Takashi Aoki, Naofumi Honda

7. Ghost busting: Making sense of non-Hermitian Hamiltonians
Carl M. Bender

8. Vanishing of the logarithmic trace of generalized Szegö projectors
Louis Boutet Monvel

9. Nonlinear Stokes phenomena in first or second order differential equations
Ovidiu Costin

10. Reconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation
Yuki Daido, Hyeonbae Kang, Gen Nakamura

11. Exact WKB analysis near a simple turning point
Eric Delabaere

12. The Borel transform
Leon Ehrenpreis

13. On the use of Z-transforms in the summation of transseries for partial differential equations
Christopher J. Howls

14. Some dynamical aspects of Painlevé VI
Katsunori Iwasaki

15. An algebraic representation for correlation functions in integrable spin chains
Michio Jimbo

16. Inverse image of D-modules and quasi-b-functions
Yves Laurent

17. The hypoelliptic Laplacian of J.-M. Bismut
Gilles Lebeau

18. Commuting differential operators with regular singularities
Toshio Oshima

19. The behaviors of singular solutions of some partial differential equations in the complex domain
Sunao ?uchi

20. Observations on the JWKB treatment of the quadratic barrier
Hujun Shen, Harris J. Silverstone

21. A role of virtual turning points and new Stokes curves in Stokes geometry of the quantum Hénon map
Akira Shudo

22. Spectral instability for non-selfadjoint operators
Johannes Sjöstrand

23. Boundary and lens rigidity, tensor tomography and analytic microlocal analysis
Plamen Stefanov, Gunther Uhlmann

24. Coupling of two partial differential equations and its application
Hidetoshi Tahara

25. Instanton-type formal solutions for the first Painlevé hierarchy
Yoshitsugu Takei

26. From exact-WKB toward singular quantum perturbation theory II
André Voros

27. WKB analysis and Poincaré theorem for vector fields
Masafumi Yoshino

Keywords: Mathematics, Integral Transforms, Operational Calculus, Ordinary Differential Equations, Partial Differential Equations, Special Functions

Publication year
Natural Sciences

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