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Asymptotics for extremal moments and monodromy of complex singularities

Summary: Asymptotics for extremal moments and monodromy of complex
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-
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.


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics