## Commutator methods for unitary operators

- Claudio Fernandez, Serge Richard, Rafael Tiedra de Aldecoa, Rafael Tiedra, C. Fern, Tiedra de Aldecoa1z
- 2012

1 Excerpt

- Published 2003

Let F denote the Fourier transform on L2(R), and let T ≡ DφMu, where Dφ ≡ FMφF−1, φ ∈ H∞(R) is inner, and |u| = 1 a.e. This paper gives a partial description of the spectral multiplicity theory of T . It is shown that T is absolutely continuous and is a bilateral shift of infinite multiplicity if φ is not a finite Blaschke product. Similar results are obtained for the (isometric) restrictions of T to the invariant subspaces L2(α,∞). Specifically, these restrictions always have absolutely continuous unitary parts, and shift parts with multiplicity equal to the multiplicity of φ.

@inproceedings{SZAJDA2003AbsoluteCO,
title={Absolute Continuity of a Class of Unitary Operators},
author={DOUGLAS C. SZAJDA},
year={2003}
}