Memoirs of the American Mathematical Society 2011; 105 pp; softcover Volume: 213 ISBN10: 0821852485 ISBN13: 9780821852484 List Price: US$74 Individual Members: US$44.40 Institutional Members: US$59.20 Order Code: MEMO/213/1003
 The authors study the moments of equilibrium measures for iterated function systems (IFSs) and draw connections to operator theory. Their main object of study is the infinite matrix which encodes all the moment data of a Borel measure on \(\mathbb{R}^d\) or \(\mathbb{C}\). To encode the salient features of a given IFS into precise moment data, they establish an interdependence between IFS equilibrium measures, the encoding of the sequence of moments of these measures into operators, and a new correspondence between the IFS moments and this family of operators in Hilbert space. For a given IFS, the authors' aim is to establish a functorial correspondence in such a way that the geometric transformations of the IFS turn into transformations of moment matrices, or rather transformations of the operators that are associated with them. Table of Contents  Notation
 The moment problem
 A transformation of moment matrices: the affine case
 Moment matrix transformation: measurable maps
 The KatoFriedrichs operator
 The integral operator of a moment matrix
 Boundedness and spectral properties
 The moment problem revisited
 Acknowledgements
 Bibliography
