Generalized factorization for Daniele-Khrapkov matrix functions -- partial indices
The authors deal with the problem of calculating the partial indices of generalized factorizations of non-rational matrix-valued functions \(G: \mathbb{R}\to \mathbb{C}^{2\times 2}\) of the form \(G= \left[\begin{smallmatrix} a &b\\ \rho^ 2 b &a\end{smallmatrix}\right]\), where \(a, b\in C(\dot\mathbb{R})\) and \(\rho\in C(\dot\mathbb{R})\) is the square-root of the quotient of two second degree polynomials such that \(a\pm \rho b\) possess bounded generalized factorizations (i.e., such that the factors and their inverses are bounded in their half-planes of analyticity). The partial indices give detailed information on the structure of the kernel and image of the associated Wiener-Hopf or Toeplitz operator in the non-canonical cases. In particular, necessary and sufficient conditions for the existence of canonical generalized factorizations are obtained.
scientific article; zbMATH DE number 765115