Ana C. Conceição

Factorization of Some Classes of Matrix Functions and the Resolvent of a Hankel Operator

The factorization of some classes of matrix-valued functions is obtained, which yields some new results for a special class of Hankel integral operators in L 2 + . For each of its elements, it is shown that the resolvent operator can be explicitly determined through a matrix factorization obtained by solving two non-homogeneous equations.

Factorization Algorithm for Some Special Non-rational Matrix Functions

We construct an algorithm that allows us to determine an effective generalized factorization of a special class of matrix functions. We use the same algorithm to analyze the spectrum of a self-adjoint operator which is related to the obtained generalized factorization.

Factorization of Matrix Functions and the Resolvents of Certain Operators

The explicit factorization of matrix functions of the form

Foreword to the Special Focus on Advances in Symbolic and Numeric Computation

{A_\gamma }(b) = \left( {\begin{array}{*{20}{c}} e&b \\ {b*}&{b*b + \gamma e} \end{array}} \right),

Symbolic Computation Applied to the Study of the Kernel of a Singular Integral Operator with Non-Carleman Shift and Conjugation

where b is an n n matrix function, e represents the identity matrix, and γ is a complex constant, is studied. To this purpose some relations between a factorization of Aγ and the resolvents of the self-adjoint operators

Computing some classes of Cauchy type singular integrals with Mathematica software

{N_ + }(b) = {P_ + }b{P_ - }b*{P_ + } and {N_ - }(b) = {P_ - }b*{P_ + }b{P_ - }