Darboux transformations for CMV matrices (Q291754)

In this monograph, the Darboux transformations for CMV matrices are explained having as first guideline the Darboux transformations for Jacobi matrices. The subjacent technical difficulties are carefully presented motivating the specific terminology used throughout the text, such like Hessenberg type matrices and zig-zag bases. Special attention is given to the measure corresponding to the Darboux transformation of a CMV matrix and to a discussion of the inverse of the Darboux transformations for CMV matrices.NEWLINENEWLINEA thorough comparison between the Darboux transformation of a Jacobi and a CMV matrix is provided reviewing both classical results and recent contributions (e.g. [\textit{M. Derevyagin} et al., Constr. Approx. 36, No. 3, 513--535 (2012; Zbl 1259.42018)]).NEWLINENEWLINEIn the latter sections, the authors explore the CMV matrices lying in different contexts as for instance ``the QR interpretation of Christoffel transformations on the unit circle based on CMV matrices '', together with further extensions.