EDP Sciences
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Volume 407, Number 1, August III 2003
Page(s) 385 - 392
Section Physical and chemical processes
DOI http://dx.doi.org/10.1051/0004-6361:20030849

A&A 407, 385-392 (2003)
DOI: 10.1051/0004-6361:20030849

Smooth maps from clumpy data: Generalizations

M. Lombardi and P. Schneider

Institut für Astrophysik und Extraterrestrische Forschung, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
(Received 30 September 2002 / Accepted 28 May 2003)

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.

Key words: methods: statistical -- methods: analytical -- methods: data analysis -- gravitational lensing

Offprint request: M. Lombardi, lombardi@astro.uni-bonn.de

© ESO 2003