Spectral factorization of measurable rectangular matrix functions and the vector-valued Riemann problem

Spectral Factorization of Non-Rational Matrix-Valued Spectral Densities

Recently, a necessary and sufficient uniform log-integrability condition has been established for the canonical spectral factorization mapping to be sequentially continuous. Under this condition, if a sequence of spectral densities converge to a limiting spectral density then the canonical spectral factors of the sequence converges to the canonical spectral factor of the limiting density. Howev...

On Spaces of Measurable Vector - Valued Functions 399 Proof

J-spectral factorization for rational matrix functions with alternative realization

In this paper, recent results by Petersen and Ran on the J-spectral factorization problem to rational matrix functions with constant signature that are not necessarily analytic at infinity are extended. In particular, a full parametrization of all J̃-spectral factors that have the same pole pair as a given square J-spectral factor is given. In this case a special realization involving a quintet ...

Generalized Rings of Measurable and Continuous Functions

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

Non-commutative Jensen and Chebyshev inequalities for measurable matrix-valued functions and measures

The idea of noncommutative averaging (that is, of a matrix-convex combination of matrixvalued functions) extends quite naturally to the integral of matrix-valued measurable functions with respect to positive matrix-valued measures. In this lecture I will report on collaborative work with F. Zhou, S. Plosker, and M. Kozdron on formulations of some classical integral inequalities (Jensen, Chebysh...