关键词: Asymptotic explansion, degenerate criticl point, hypersurfave, distribution-valued meromorphic function, analytic extention

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