Inverse problem for one-dimensional fractal measures via iterated function systems and the moment method
- 1 December 1990
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 6 (6) , 885-896
- https://doi.org/10.1088/0266-5611/6/6/002
Abstract
The author shows how to reconstruct measures with compact support on the real line using p-balanced measures associated with linear homogeneous iterated function systems and requiring that the first 2s+1 moments are equal to those of the original measure. The author proves that the sequence of approximating measures obtained in such a way converge in the Hutchinson metric ( omega *-topology). A sufficient condition for the convergence of the support of the measure in the Hausdorff metric is also stated.Keywords
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