Smooth maps from clumpy data: generalizations

Details Smooth maps from clumpy data: generalizations Smooth maps from clumpy data: generalizations

2003-06-10

arxiv.org/abs/astro-ph/0306202v1

Astron.Astrophys. 407 (2003) 385

Astronomy and Astrophysics

Astrophysics

9 pages, 3 figures, A&A in press

Scientific paper

10.1051/0004-6361:20030849

In a series of papers (Lombardi & Schneider 2001, 2002) we studied in detail the statistical properties of an interpolation technique widely used in astronomy. In particular, we considered the average interpolated map and its covariance under the hypotheses that the map is obtained by smoothing unbiased measurements of an unknown field, and that the measurements are uniformly distributed on the sky. In this paper we generalize the results obtained to the case of observations carried out only on a finite field and distributed on the field with a non-uniform density. These generalizations, which are required in many astronomically relevant cases, still allow an exact, analytical solution of the problem. We also consider a number of properties of the interpolated map, and provide asymptotic expressions for the average map and the two-point correlation function which are valid at high densities.

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