A fixed point theorem for moment matrices of selfsimilar measures
Abstract
We consider the selfsimilar measure on the complex plane 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 selfsimilar measure. As a consequence, we obtain a very efficient algorithm to compute the moment matrix of the selfsimilar 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.
 Publication:

Journal of Computational and Applied Mathematics
 Pub Date:
 October 2007
 Bibcode:
 2007JCoAM.207..352E
 Keywords:

 Selfsimilar measures;
 Orthogonal polynomials;
 Moment matrix;
 Fixed point theorem