Volume 24, pp. 79-87, 2006.

Moment matrix of self-similar measures

C. Escribano, M. A. Sastre, and E. Torrano


We give in this paper an expression for the moment matrix associated to a self-similar measure given by an Iterated Function Systems (IFS). This expression translates the self-similarity property of a measure to its moment matrix. This matrix relation shows that the properties of a measure are reflected, not only in the equation of its Jacobi matrix, as stated in Krein theorem, but also in the moment matrix.

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Key words

self-similar measures, orthogonal polynomials, moment matrix

AMS subject classifications

42C05, 28A80

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