Factorization Algorithm for Some Special Matrix Functions

TL;DR: This paper constructed an algorithm, [SInt], for computing some classes of Cauchy type singular integrals on the unit circle and shows how the factorization algorithm described in Conceição et al. (2010) allowed the algorithm to be constructed and implemented.

TL;DR: This work uses the CAS Mathematica to implement for the first time on a computer analytical algorithms developed by us and others within the Operator Theory, to explore the spectra of several classes of singular integral operators.

TL;DR: In this paper, the authors present a series devoted to the publication of current research in operator theory, with particular emphasis on applications to classical analysis and the theory of integral equations, as well as to numerical analysis, mathematical physics and mathematical methods in electrical engineering.

TL;DR: The Factorization of Rational Matrix Functions as discussed by the authors is a generalization of matrix function factorization relative to a contour, and generalized factorization of rational matrix functions is also related to generalized factorization.

TL;DR: In this article, the authors characterized the set of extended eigenvalues of an operator A for finite dimensional spaces, finite rank operators, Jordan blocks, and C0 contractions, and showed that the commutant of A coincides with that of A if the extended point spectrum of A does not contain any n-th root of unity other than 1.