Necessary and sufficient conditions for Hurwitz (resp. Schur) stability of convex combination of two complex polynomials are introduced in the paper. The conditions are more general than those given in [2] and supplement work [3].
The paper concerns the spectral theory for a class of non-self-adjoint block convolution operators. We mainly discuss the spectral representations of such operators. It is considered the general case of operators defined on Banach spaces. The main results are applied to periodic Jacobi matrices.
We describe some spectral representations for a class of non-self-adjoint banded Jacobi-type matrices. Our results extend those obtained by P.B. Naïman for (two-sided infinite) periodic tridiagonal Jacobi matrices.
