Formal Symbol Type Solutions of Fuchsian Microdifferential Equations

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J. Math. Sci. Univ. Tokyo
Vol. 9 (2002), No. 4, Page 565--626.

Kataoka, Kiyoomi ; Satoh, Yoshiaki
Formal Symbol Type Solutions of Fuchsian Microdifferential Equations
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
We construct a basis of solutions for a micro-differ\-ential equation with Fuchsian singularities in microfunctions with one holomorphic parameter. More precisely, we construct solutions written by formal symbols with one holomorphic parameter. For such an equation of order $m$, we get $(m-1)$-regular formal symbols and one singular formal symbol; the latter is not holomorphic along the Fuchsian singularities but has boundary values in the sense of microfunctions.

Mathematics Subject Classification (2000): Primary 35A27; Secondary 35S99

Mathematical Reviews Number: MR1947483

Received: 2001-05-29

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