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/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Matrix Szego biorthogonal polynomials for quasi-definite matrices of measuresare studied. For matrices of Holder weights a Riemann-Hilbert problem isuniquely solved in terms of the matrix Szego polynomials and its Cauchytransforms. The Riemann-Hilbert problem is given as an appropriate frameworkfor the discussion of the Szego matrix and the associated Szego recursionrelations for the matrix orthogonal polynomials and its Cauchy transforms.Pearson type differential systems characterizing the matrix of weights arestudied. These are linear systems of ordinary differential equations which arerequired to be monodromy free. Linear ordinary differential equations for thematrix Szego polynomials and its Cauchy transforms are derived. It is shown howthese Pearson systems lead to nonlinear difference equations for the Verblunskymatrices and two examples, of Fuchsian and non-Fuchsian type, are considered.For both cases a new matrix version of the discrete Painlev\'e II equation forthe Verblunsky matrices is found. Reductions of these matrix discrete PainleveII systems presenting locality are discussed.

Matrix biorthogonal polynomials in the unit circle: Riemann-Hilbert problem and matrix discrete Painleve II system