A fixed point theorem for moment matrices of self-similar measures

Authors:
C. Escribano;M. A. Sastre;E. Torrano
Affiliations:
Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica de Madrid, Spain;Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica de Madrid, Spain;Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica de Madrid, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 3
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Abstract

We consider the self-similar measure on the complex plane C associated to an iterated function system (IFS) with probabilities. From this IFS we define an operator in a complete metric space of infinite matrices. Using the expression obtained in a previous work of the authors, we prove that this operator has as fixed point the moment matrix of the self-similar measure. As a consequence, we obtain a very efficient algorithm to compute the moment matrix of the self-similar measure. Finally, in order to estimate the rate of convergence of the algorithm, we find an upper bound of the norm of this contractive operator.