A GENERALIZATION OF THE MOMENT PROBLEM TO A COMPLEX MEASURE SPACE AND AN APPROXIMATION TECHNIQUE USING BACKWARD MOMENTS

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One traditionally considers positive measures in the moment problem. However, this restriction makes its theory and application limited. The main purpose of this paper is to generalize it to deal with complex measures. More precisely, the theory of the truncated moment problem is extended to include complex measures. This extended theory provides considerable flexibility in its applications. In fact, we also develop an approximation technique based on control of moments. The key idea is to use the heat equation as a link that connects the generalized moment problem and this approximation technique. The backward moment of a measure is introduced as the moment of a solution to the heat equation at a backward time and then used to approximate the given measure. This approximation gives a geometric convergence order as the number of moments under control increases. Numerical examples are given that show the properties of approximation technique.
Publisher
AMER INST MATHEMATICAL SCIENCES
Issue Date
2011-05
Language
English
Article Type
Article
Keywords

VISCOUS BURGERS-EQUATION; NONLINEAR DIFFUSION; CONVERGENCE; ASYMPTOTICS

Citation

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.30, no.1, pp.187 - 207

ISSN
1078-0947
URI
http://hdl.handle.net/10203/103493
Appears in Collection
MA-Journal Papers(저널논문)
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