Ellis–Gohberg identities for certain orthogonal functions I: Block matrix generalizations and ℓ2ℓ2-setting

Generalizations of identities for certain orthogonal functions due to Ellis–Gohberg (1992) and Ellis (2011) are presented. The matrix-valued version of the Ellis identity is derived, and a more general 2×22×2 block matrix version is obtained. The latter contains the (matrix-valued versions of the) Ellis–Gohberg and Ellis identities as sub-identities. Intertwining relations involving shifts are used systematically. This allows us to derive the results in an ℓ2ℓ2-setting rather than in an ℓ1ℓ1-setting.