arXiv subjects

Conrad Mädler

Publications and source records attributed to Conrad Mädler.

21 records · Page 2Linked to original sources

arXiv2015

Rational $q\times q$ Carathéodory Functions and Central Non-negative Hermitian Measures

We give an explicit representation of central measures corresponding to finite Toeplitz non-negative definite sequences of complex $q\times q$ matrices. Such measures are intimately connected to central $q\times q$ Carathéodory functions. This enables us to prove an explicit representation of the non-stochastic spectral measure of an arbitrary multivariate autoregressive stationary sequence in terms of the covariance sequence.

math.CV↗

arXiv2015

On Matrix-Valued Stieltjes Functions with an Emphasis on Particular Subclasses

The paper deals with particular classes of $q\times q$ matrix-valued functions which are holomorphic in $\mathbb{C}\setminus[α,+\infty)$, where $α$ is an arbitrary real number. These classes are generalizations of classes of holomorphic complex-valued functions studied by Kats and Krein [17] and by Krein and Nudelman [19]. The functions are closely related to truncated matricial Stieltjes problems on the interval $[α,+\infty)$. Characterizations of these classes via integral representations are presented. Particular emphasis is placed on the discussion of the Moore-Penrose inverse of these matrix-valued functions.

math.CV↗

arXiv2012

On a Simultaneous Approach to the Even and Odd Truncated Matricial Hamburger Moment Problems

The main goal of this paper is to achieve a simultaneous treatment of the even and odd truncated matricial Hamburger moment problems in the most general case. In the odd case, these results are completely new for the matrix case, whereas the scalar version was recently treated by V. A. Derkach, S. Hassi and H. S. V. de Snoo. The even case was studied earlier by G.-N. Chen and Y.-J. Hu. Our approach is based on Schur analysis methods. More precisely, we use two interrelated versions of Schur-type algorithms, namely an algebraic one and a function-theoretic one. The algebraic version was worked out in a former paper of the authors. It is an algorithm which is applied to finite or infinite sequences of complex matrices. The construction and investigation of the function-theoretic version of our Schur-type algorithm is a central theme of this paper. This algorithm will be applied to relevant subclasses of holomorphic matrix-valued functions of the Herglotz-Nevanlinna class. Using recent results on the holomorphicity of the Moore-Penrose inverse of matrix-valued Herglotz-Nevanlinna functions, we obtain a complete description of the solution set of the moment problem under consideration in the most general situation.

math.CV↗