| Titre : | Iterated function systems, moments, and transformations of infinite matrices | | Type de document : | texte imprimé | | Auteurs : | Palle E.T. JORGENSEN, Auteur ; Keri A. KORNELSON, Auteur ; Karen L. SHUMAN, Auteur | | Editeur : | Providence, R. I. [Etats Unis] : American Mathematical Society | | Année de publication : | cop. 2011 | | Collection : | Memoirs of the American Mathematical Society, ISSN 0065-9266 num. 1003 | | Importance : | IX-105 p. | | ISBN/ISSN/EAN : | 978-0-8218-5248-4 | | Langues : | Anglais | | Catégories : | 28A12
34B45
42A82
42C05
| | Mots-clés : | matrice infinie transformation méthode itérative | | Résumé : | We study the moments of equilibrium measures for iterated function systems (IFSs) and draw connections to operator theory. Our main object of study is the infinite matrix which encodes all the moment data of a Borel measure on ?d or ?. To encode the salient features of a given IFS into precise moment data, we 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, our 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.
We first examine the classical existence problem for moments, culminating in a new proof of the existence of a Borel measure on ? or ? with a specified list of moments. Next, we consider moment problems associated with affine and non-affine IFSs. Our main goal is to determine conditions under which an intertwining relation is satisfied by the moment matrix of an equilibrium measure of an IFS.
| | Note de contenu : | bibliogr. |
Iterated function systems, moments, and transformations of infinite matrices [texte imprimé] / Palle E.T. JORGENSEN, Auteur ; Keri A. KORNELSON, Auteur ; Karen L. SHUMAN, Auteur . - Providence, R. I. (Etats Unis) : American Mathematical Society, cop. 2011 . - IX-105 p.. - ( Memoirs of the American Mathematical Society, ISSN 0065-9266; 1003) . ISBN : 978-0-8218-5248-4 Langues : Anglais | Catégories : | 28A12
34B45
42A82
42C05
| | Mots-clés : | matrice infinie transformation méthode itérative | | Résumé : | We study the moments of equilibrium measures for iterated function systems (IFSs) and draw connections to operator theory. Our main object of study is the infinite matrix which encodes all the moment data of a Borel measure on ?d or ?. To encode the salient features of a given IFS into precise moment data, we 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, our 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.
We first examine the classical existence problem for moments, culminating in a new proof of the existence of a Borel measure on ? or ? with a specified list of moments. Next, we consider moment problems associated with affine and non-affine IFSs. Our main goal is to determine conditions under which an intertwining relation is satisfied by the moment matrix of an equilibrium measure of an IFS.
| | Note de contenu : | bibliogr. |
|  |
Affiner la recherche Interroger des sources externesIterated function systems, moments, and transformations of infinite matrices / Palle E.T. JORGENSEN (cop. 2011)
