On inhomogeneous self-similar measures and their $L^{q}$ spectra

Przemysław Liszka¹

¹ Institute of Mathematics University of Silesia 40-007 Katowice, Poland

Annales Polonici Mathematici, Tome 109 (2013) no. 1, pp. 75-92.

Résumé

Let $S_i:\mathbb {R}^d\rightarrow \mathbb {R}^d$ for $i=1,\dots ,N$ be contracting similarities, let $(p_1,\dots , p_N,p)$ be a probability vector and let $\nu $ be a probability measure on $\mathbb {R}^d$ with compact support. It is well known that there exists a unique inhomogeneous self-similar probability measure $\mu $ on $\mathbb {R}^d$ such that $\mu =\sum _{i=1}^{N}{p_i\mu \circ S_i^{-1}} + p\nu $.

Détail

DOI : 10.4064/ap109-1-6

Keywords: mathbb rightarrow mathbb dots contracting similarities dots probability vector probability measure mathbb compact support known there exists unique inhomogeneous self similar probability measure mathbb sum circ satisfactory estimates lower upper bounds spectra inhomogeneous self similar measures which there countable number contracting similarities probabilities considered particular generalise results obtained olsen snigireva nonlinearity partial answer question paper