Rocky Mountain Journal of Mathematics

Invariant sets for QMF functions

Adam Jonsson

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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

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

First available in Project Euclid: 30 December 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Scaling functions Markov processes invariant sets


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.

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