Rocky Mountain Journal of Mathematics

Invariant sets for QMF functions

Adam Jonsson

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Abstract

A quadrature mirror filter (QMF) function can be considered as the transition function for a Markov process on the unit interval. The QMF functions that generate scaling functions for multiresolution analyses are then distinguished by properties of their invariant sets. By characterizing these sets, we answer in the affirmative a question raised by Gundy.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 8 (2018), 2559-2571.

Dates
First available in Project Euclid: 30 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1546138821

Digital Object Identifier
doi:10.1216/RMJ-2018-48-8-2559

Mathematical Reviews number (MathSciNet)
MR3894993

Zentralblatt MATH identifier
06999274

Subjects
Primary: 37B10: Symbolic dynamics [See also 37Cxx, 37Dxx] 37C70: Attractors and repellers, topological structure 42C40: Wavelets and other special systems

Keywords
Scaling functions Markov processes invariant sets

Citation

Jonsson, Adam. Invariant sets for QMF functions. Rocky Mountain J. Math. 48 (2018), no. 8, 2559--2571. doi:10.1216/RMJ-2018-48-8-2559. https://projecteuclid.org/euclid.rmjm/1546138821


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