Acta mathematica scientia,Series B ›› 1999, Vol. 19 ›› Issue (2): 127-137.
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JI Min-You, ZHANG Guan-Beng
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Supported by NNSFC(China)
Abstract:
In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE, this paper studies the asymtotic expansion of Dirac-type distribution associated with a class of hypersurfaces F(x) with degenerate criticak points and proves that [F(x)]+ is a distribution-valued meromorphc of \lamda ( -C under some assunotion on F(x).Next,the authors use the Normal form theory of Arnold and prove that for a hypersuface F(x)=0 with A_\mu type degenerate critical point at x=0, F_+ is a distribution-valued mermorphic function of \lamda
Key words: Asymptotic explansion, degenerate criticl point, hypersurfave, distribution-valued meromorphic function, analytic extention
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JI Min-You, ZHANG Guan-Beng. Asymptotic Expansion of Dirac-type Distribution Associates with a class of Hypersurfaces with Degenerated Critical Points[J].Acta mathematica scientia,Series B, 1999, 19(2): 127-137.
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