Reducibility of the wavelet representation associated to the Cantor set

Abstract

We answer a question by Judith Packer about the irreducibility of the wavelet representation associated to the Cantor set. We prove that if the QMF filter does not have constant absolute value, then the wavelet representations is reducible.

References in corpus (2)

• Martingales, endomorphisms, and covariant systems of operators in Hilbert space
• Irreducible wavelet representations and ergodic automorphisms on solenoids

Cited by in corpus (2)

• Irreducible wavelet representations and ergodic automorphisms on solenoids
• Decomposition of wavelet representations and Martin boundaries