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Summary: Semi-local micro-differential theory and computations of moments
of semi-algebraic domains
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,
34M15, 34M35.
Keywords: extremal L-problem of moments, Laplace transform, Gauss-
Manin connexion, microdifferential system.
Abstract
In the extremal n-variable L-moment problem, the solution (=the
characteristic function of {p < 0},) p a polynomial, is determined by
finitely many moments, in a set A.
In [23], for quadrature domains (n = 2), the reduction of all moments
to the moments in A is implicit in the reconstruction of p using hyponor-
mal operators.
For n 2, assuming that the complexified of p has only isolated critical
points for its singularities, we show that the local algorithm [22] which
reduces to the moments in a base extends to the global case, with equality
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