Algebraic analysis of differential equations: from by T. Aoki, H. Majima, Y. Takei, N. Tose

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

This quantity includes 23 articles on algebraic research of differential equations and comparable issues, so much of that have been provided as papers on the foreign convention "Algebraic research of Differential Equations – from Microlocal research to Exponential Asymptotics" at Kyoto collage in 2005. Microlocal research and exponential asymptotics are in detail hooked up and supply strong instruments which have been utilized to linear and non-linear differential equations in addition to many comparable fields resembling actual and complicated research, fundamental transforms, spectral concept, inverse difficulties, integrable structures, and mathematical physics. The articles contained right here current many new effects and ideas, delivering researchers and scholars with necessary feedback and instructive suggestions 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 celebration of Professor Kawai's sixtieth birthday as a token of deep appreciation of the $64000 contributions he has made to the sphere. Introductory notes at the medical works of Professor Kawai also are included.

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Additional 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]

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Pham: Resurgence, quantized canonical transformations, and multiinstanton expansions, Algebraic Analysis, vol. II, Acad. Press, 1988, pp. 699-726. S. Sasaki: On the role of virtual turning points in the deformation of higher order linear ordinary differential equations, RIMS Koukyuuroku, (ISSN 1880-2818), No. 1433, 2005, pp. 27-64. , pp. 65-109. ) Virtual turning points [SKK] [Sh] [S] [T] [V] [Z] 43 M. Sato, T. Kawai and M. Kashiwara: Microfunctions and pseudodifferential equations, Lect. , No. 287, Springer, 1973, pp.

4). If f0 , f1 , . . , fl is a tame regular sequence at x0 , then we have H k (L·x0 ) = 0 for every k ≤ l. If we look at the l-th order part of the Koszul complex, we have the following: Theorem 4. Suppose that H l (L·x0 ) = 0 holds. Then fl is not a zero divisor on Ox0 /(f0 , . . , fl−1 ). 48 Takashi Aoki and Naofumi Honda Combining Theorems 3 and 4 yields Theorem 5. Let f0 , f1 , . . , fl be elements in Ox0 . Then the following two conditions are equivalent: 1. The sequence f0 , f1 , . . , fl is a tame regular sequence at x0 .

O] K. Okamoto: Isomonodromic deformation and Painlev´e equations, and the Garnier systems, J. Fac. Sci. Univ. Tokyo, Sect. IA, 33(1986), 575–618. [P] F. Pham: Resurgence, quantized canonical transformations, and multiinstanton expansions, Algebraic Analysis, Vol. II, Academic Press, 1988, pp. 699–726. [V] A. Voros: The return of the quartic oscillator. The complex WKB method, Ann. Inst. Henri Poincar´e, 39(1983), 211–338. [Z] J. Zinn-Justin: Instantons in quantum mechanics: Numerical evidence for a conjecture, J.

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