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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. e-mail: gputinar@att.net
Mathematics Sciences Classification [2000]44A60, 65R32, 14P05, 34M35.
Keywords: L-problem 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 n-dimensional L-moment problem, linearly in terms of a finite set
of generating moments, in the context of dynamic (i.e. time-dependent)
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.
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