By T. Aoki, H. Majima, Y. Takei, N. Tose

This quantity comprises 23 articles on algebraic research of differential equations and similar themes, such a lot of which have been awarded as papers on the overseas convention "Algebraic research of Differential Equations – from Microlocal research to Exponential Asymptotics" at Kyoto college in 2005. Microlocal research and exponential asymptotics are in detail hooked up and supply robust instruments which were utilized to linear and non-linear differential equations in addition to many similar fields comparable to genuine and intricate research, indispensable transforms, spectral conception, inverse difficulties, integrable platforms, and mathematical physics. The articles contained the following current many new effects and concepts, supplying researchers and scholars with beneficial feedback and instructive tips for his or her paintings. This quantity is devoted to Professor Takahiro Kawai, who's one of many creators of microlocal research and who brought the means of microlocal research into exponential asymptotics. This commitment is made at the party of Professor Kawai's sixtieth birthday as a token of deep appreciation of the real contributions he has made to the sphere. Introductory notes at the clinical works of Professor Kawai also are included.

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**Extra info for Algebraic analysis of differential equations: from microlocal analysis to exponential asymptotics; Festschrift in honor Prof. Takahiro Kawai [on the occasion of his sixtieth birthday]**

**Sample text**

This result of Kawai visualizes in a clear-cut way the existence of intimate relation between exact WKB analysis and microlocal analysis in the very fundamental part of the theory. Furthermore, pursuing Sato’s suggestion that the argument of Voros should be regarded as a tool for understanding the general global structure of diﬀerential equations beyond the framework of eigenvalue problems, we next succeeded in ﬁnding a recipe for explicit computation of the monodromy group of a second order diﬀerential equation of Fuchsian type by applying exact WKB analysis ([95]); it claims that the monodromic structure of (1) can be described in terms of contour integrals of the logarithmic derivative of the WKB solution (to be more precise, of its odd part; see Chapters 2 and 3 of our monograph [B3] for details).

A. Shudo: A recipe for ﬁnding Stokes geometry in quantized H´enon map, RIMS Koukyuuroku, (ISSN 1880-2818), No. 1433, 2005, pp. 110-118. H. J. Silverstone: JWKB connection-formula problem revisited via Borel summation, Phys. Rev. , 55 (1985), 2523-2526. Y. Takei: Exact WKB analysis, and exact steepest descent method, – A sequel to “Algebraic analysis of singular perturbations”, Sˆ ugaku, 55 (2003), 350-367. (In Japanese. ) A. Voros: The return of the quartic oscillator. The complex WKB method, Ann.

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