MPEJ Volume 15, No. 1, 19 pp.
Received: Dec 31, 2007. Revised: Jun 2, 2009. Accepted: Jul 16, 2009.


S. Dostoglou, J.D. Kahl
Approximation of homogeneous measures in the 2-Wasserstein metric


ABSTRACT: It is shown that, on certain weighted spaces of vector fields on R^3,
any homogeneous measure of finite energy density and dissipation can be
approximated in the second Wasserstein distance by homogeneous measures
supported by finite trigonometric polynomials of increasing period and degree.
In particular, the periodic correlation functions of the approximation converge
uniformly on compact sets of R^3 to the correlation function of the given
measure.


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