  A kernel method is proposed to estimate the condensed density of the
generalized eigenvalues of pencils of Hankel matrices whose elements have a
joint noncentral Gaussian distribution with nonidentical covariance. These
pencils arise when the complex exponentials approximation problem is considered
in Gaussian noise. Several moments problems can be formulated in this framework
and the estimation of the condensed density above is the main critical step for
their solution. It is shown that the condensed density satisfies approximately
a diffusion equation, which allows to estimate an optimal bandwidth. It is
proved by simulation that good results can be obtained even when the
signal-to-noise ratio is so small that other methods fail.
