Iterated function systems, moments, and transformations of infinite matrices / Palle E. T. Jorgensen, Keri A. Kornelson, Karen L. Shuman

Auteur: Jørgensen, Palle E. T. (1947-) - AuteurCo-auteur: Kornelson, Keri A. (1967-) - Auteur ; Shuman, Karen L. (1973-) - AuteurType de document: MonographieCollection: Memoirs of the American Mathematical Society ; 1003Langue: anglaisPays: Etats UnisÉditeur: Providence (R.I.) : American Mathematical Society, 2011Description: 1 vol. (IX-105 p.) ; 26 cm ISBN: 9780821852484 ; br. ISSN: 0065-9266Résumé: 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 ℝd or 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. (Source : AMS).Bibliographie: Bibliogr. p. 103-105. Sujets MSC: 47-02 Operator theory -- Research exposition (monographs, survey articles)
47Lxx Operator theory -- Linear spaces and algebras of operators
60J10 Probability theory and stochastic processes -- Markov processes -- Markov chains (discrete-time Markov processes on discrete state spaces)
60J20 Probability theory and stochastic processes -- Markov processes -- Applications of Markov chains and discrete-time Markov processes on general state spaces
28A12 Measure and integration -- Classical measure theory -- Contents, measures, outer measures, capacities
34B45 Ordinary differential equations -- Boundary value problems -- Boundary value problems on graphs and networks
En-ligne: ArXiv
Location Call Number Status Date Due
Couloir 06776-01 / Séries AMS (Browse Shelf) Available

Bibliogr. p. 103-105

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 ℝd or 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. (Source : AMS)

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