English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Matrix orthogonal Laurent polynomials in the unit circle and the theory ofToda-like integrable systems are connected using the Gauss--Borel factorizationof two, left and a right, Cantero-Morales-Velazquez block moment matrices,which are constructed using a quasi-definite matrix measure. A blockGauss-Borel factorization problem of these moment matrices leads to two sets ofbiorthogonal matrix orthogonal Laurent polynomials and matrix Szeg\H{o}polynomials, which can be expressed in terms of Schur complements of borderedtruncations of the block moment matrix. The corresponding block extension ofthe Christoffel-Darboux theory is derived. Deformations of the quasi-definitematrix measure leading to integrable systems of Toda type are studied. Theintegrable theory is given in this matrix scenario; wave and adjoint wavefunctions, Lax and Zakharov-Shabat equations, bilinear equations and discreteflows --connected with Darboux transformations--. We generalize the integrableflows of the Cafasso's matrix extension of the Toeplitz lattice for theVerblunsky coefficients of Szeg\H{o} polynomials. An analysis of the Miwashifts allows for the finding of interesting connections betweenChristoffel--Darboux kernels and Miwa shifts of the matrix orthogonal Laurentpolynomials.

Matrix Orthogonal Laurent Polynomials on the Unit Circle and Toda Type Integrable Systems