Ellis-Gohberg identities for certain orthogonal functions. I: Block matrix generalizations and \({\ell}^2\)-setting (Q692577)

The authors generalize identities for certain orthogonal functions due to Ellis-Cohberg (1992) and Ellis (2011). The main results are Theorems 1.3 and 1.4. The first one is a matrix valued version of a theorem given by Ellis (2012) and the second provides a stronger \(2\times 2\) block-matrix identity. For the proofs of the theorems Hilbert space methods are used and intertwining relations involving shift operators, thus the results can be obtained in an \(\ell^2\)-setting rather than in an \({l^2}\)-setting.