Y. Kamp

The Nevanlinna–Pick Problem for Matrix-Valued Functions

This paper contains a detailed treatment of the Nevanlinna–Pick interpolation problem for matrix-valued functions. A close relationship with the trigonometric moment problem is put into light. Matrix extensions of Pick’s solvability criterion and Nevanlinna’s iterative algorithm are presented. Necessary and sufficient conditions are obtained for uniqueness of the solution of the infinite interpolation problem. The approach is essentially based upon the theories of J-contractive transformations and of Weyl matrix circles.

Schur Parametrization of Positive Definite Block-Toeplitz Systems

The parameters occurring in Szego’s recurrence relations associated with a class C function are known to be the same as the Schur parameters of the corresponding class S function. The present paper contains a matrix extension of this result. Certain important questions about the matrix classes S and C, related to spectral factorization, are studied by means of their Schur–Szego parameters.

A method of matrix inverse triangular decomposition based on contiguous principal submatrices

Abstract An algorithm is presented which performs the triangular decomposition of the inverse of a given matrix. The method is applicable to any matrix all contiguous principal submatrices of which are nonsingular. The algorithm is particularly efficient when the matrix has certain partial symmetries exhibited by the Toeplitz structure.

On the role of the partial trigonometric moment problem in AR speech modelling

The partial trigonometric moment problem is shown to provide a unifying framework for several speech modelling techniques, such as the classical LPC antoregressive model, the line spectral pairs and composite sinusoidal waves models, and the Toeplitz eigenvector model for formant extraction, From a mathematical viewpoint, this moment problem can be identified to an extension problem in the class of impedance functions or equivalently in the class of nonnegative definite Toeplitz matrices.

Generalized Schur Representation of Matrix-Valued Functions

The generalized Schur representation of a function matrix

Half-Plane Minimization of Matrix-Valued Quadratic Functionals

\Omega ( e^{i\theta } )

An equivalence between bounded multivariable functions and a class of bounded single-variable functions

satisfying

Planar Least-Squares Inverse Polynomials. Part II: Asymptotic Behavior

\| \Omega \|_\infty \leqq1

SPEECH MODELLING AND THE TRIGONOMETRIC MOMENT PROBLEM

is investigated in connection with certain results concerning the extensions of block-Hankel operators acting on Hilbert spaces. Various properties of such representations are elucidated, including a parametrization of

Characterization theorems for bounded and positive two‐variable functions

\Omega ( e^{i\theta } )