In this survey we establish bijective correspondences between the following classes of objects: (1) β−1 and {βn}n=0∞, with βn∈Cp×p for n=−1,0,..., β−1 unitary, ∥βj∥<1 for j≥0 and ∑j=0∞∥βj∥<∞; (2) A unitary matrix β−1∈Cp×p and a spectral density Δ belonging to the Wiener algebra Wp×p with Δ(ζ)≻0 for all ζ on the unit circle T; (3) CMV matrices based on a unitary matrix β−1∈Cp×p and a spectral density Δ that meets the constraints in (2); (4) scattering matrices that belong to the Wiener algebra Wp×p; (5) a class of solutions of an associated matricial Nehari problem.
1
The Weizmann Institute of Science, Rehovot, Israel
2
Ben-Gurion University of the Negev, Beer-Sheva, Israel
Harry Dym; David P. Kimsey. CMV matrices, a matrix version of Baxter's theorem, scattering and de Branges spaces. EMS surveys in mathematical sciences, Tome 3 (2016) no. 1, pp. 1-105. doi: 10.4171/emss/14
@article{10_4171_emss_14,
author = {Harry Dym and David P. Kimsey},
title = {CMV matrices, a matrix version of {Baxter's} theorem, scattering and de {Branges} spaces},
journal = {EMS surveys in mathematical sciences},
pages = {1--105},
year = {2016},
volume = {3},
number = {1},
doi = {10.4171/emss/14},
url = {http://geodesic.mathdoc.fr/articles/10.4171/emss/14/}
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