Exploring the spectra of some classes of paired singular integral operators: the scalar and matrix cases

Abstract

The main goal of this paper is to present some results on the spectra of paired singular integral operators with essentially bounded matrix functions coefficients, defined on the unit circle. In addition, we present the spectral algorithms [ASpecPaired-Scalar] and [ASpecPaired-Matrix] which use the symbolic and numeric computation capabilities of the computer algebra system Mathematica to check, for each considered paired singular integral operator with rational coefficients, if a complex number (chosen arbitrarily) belongs to its spectrum. Some nontrivial examples computed with these algorithms are presented.