Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-30T22:25:59.447Z Has data issue: false hasContentIssue false
  • English
  • Français

ITERATED FUNCTION SYSTEMS WITH OVERLAPS AND SELF-SIMILAR MEASURES

Published online by Cambridge University Press:  19 March 2001

KA-SING LAU ,
SZE-MAN NGAI  and
HUI RAO
KA-SING LAU
Affiliation:
Department of Mathematics, Chinese University of Hong Kong, Hong Kong; [email protected]
SZE-MAN NGAI
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA Current address of S. M. Ngai: Department of Mathematics, Georgia Southern University, Statesboro, GA 30460, USA; [email protected]
HUI RAO
Affiliation:
Department of Mathematics, Wuhan University, Wuhan 430072, China; [email protected]
Get access

Abstract

The paper considers the iterated function systems of similitudes which satisfy a separation condition weaker than the open set condition, in that it allows overlaps in the iteration. Such systems include the well-known Bernoulli convolutions associated with the PV numbers, and the contractive similitudes associated with integral matrices. The latter appears frequently in wavelet analysis and the theory of tilings. One of the basic questions is studied: the absolute continuity and singularity of the self-similar measures generated by such systems. Various conditions to determine the dichotomy are given.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 63 , Issue 1 , February 2001 , pp. 99 - 116
Copyright
The London Mathematical Society 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)