 
Summary: Asymptotics for extremal moments and monodromy of complex
singularities
Gabriela Putinar
Address: Department of Mathematics, University of California, Santa Bar
bara, CA 93106, U.S.A. email: gputinar@att.net
Mathematics Sciences Classification [2000]44A60, 65R32, 14P05, 34M35.
Keywords: Lproblem of moments, Fourier transform, monodromy, asymp
totics
Abstract
We present a finite algorithm for the computation of any moment of
the solution (= the characteristic function of {p < 1}, with p a polynomial,
assumed to have isolated (complex) critical points) of the truncated ex
tremal ndimensional Lmoment problem, linearly in terms of a finite set
of generating moments, in the context of dynamic (i.e. timedependent)
moments. We find that a system of such generators is provided by the
moments corresponding to a basis for R[x1, ..., xn]/I p , where I p is the
gradient ideal of p. From this, based on the algebraic formalism for asymp
totics of the Fourier transform (Malgrange, 1974), we obtain computations
for the coefficients of the asymptotic expansions for the moments in terms
of the generators and the monodromy of p.
