Abstract
We study the reducibility of the wavelet representation associated to various QMF filters, including those associated to Cantor sets. We show there are connections between this problem, the harmonic analysis of transfer operators and the ergodic properties of shifts on solenoids. We prove that if the QMF filter does not have constant absolute value, then the wavelet representations is reducible.
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Acknowledgements
This research was supported in part by The Swedish Foundation for International Cooperation in Research and Higher Education (STINT), The Swedish Research Council, The Swedish Royal Academy of Sciences and The Crafoord Foundation. The second author also is grateful to Institut Mittag-Leffler for support of his participation in Quantum Information Theory program in Autumn 2010, which has been beneficial for completion of this work.
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Dutkay, D.E., Silvestrov, S. (2012). Wavelet Representations and Their Commutant. In: Åström, K., Persson, LE., Silvestrov, S. (eds) Analysis for Science, Engineering and Beyond. Springer Proceedings in Mathematics, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20236-0_9
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DOI: https://doi.org/10.1007/978-3-642-20236-0_9
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