Ellis-Gohberg Identities for Certain Orthogonal Functions II: Algebraic Setting and Asymmetric Versions
M. A. Kaashoek, Frederik van Schagen · Mathematical Proceedings of the Royal Irish Academy · 2013
In this paper the Ellis-Gohberg identity and its 2 × 2 block matrix generalization are put into an abstract algebraic setting inspired by the band method. As an application we obtain asymmetric versions of these identities, both in the discrete and the continuous time case. Furthermore we show that these asymmetric versions allow us to derive alternative inversion formulas for certain Toeplitz plus Hankel operators, again both in the discrete and the continuous time case.