In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE,this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypersu...In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE,this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypersurfaces F(x)with degenerate critical points and proves that[F(x)](+)(lambda)is a distribution-valued meromorphic of lambda is an element of C under some assumptions on F(x).Next,the authors use the Normal form theory of Arnold and prove that for a hypersurface F(x)=0 with A(mu)type degenerate critical point at x=0,F-+(lambda)is a distribution-valued meromorphic function of lambda.展开更多
基金Supported by National Natural Science Foundation of China
文摘In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE,this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypersurfaces F(x)with degenerate critical points and proves that[F(x)](+)(lambda)is a distribution-valued meromorphic of lambda is an element of C under some assumptions on F(x).Next,the authors use the Normal form theory of Arnold and prove that for a hypersurface F(x)=0 with A(mu)type degenerate critical point at x=0,F-+(lambda)is a distribution-valued meromorphic function of lambda.
