Invariant sets for QMF functions

Adam Jonsson

doi:10.1216/RMJ-2018-48-8-2559

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Home > Journals > Rocky Mountain J. Math. > Volume 48 > Issue 8 > Article

2018 Invariant sets for QMF functions

Adam Jonsson

Rocky Mountain J. Math. 48(8): 2559-2571 (2018). DOI: 10.1216/RMJ-2018-48-8-2559

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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.