The twofold Ellis-Gohberg inverse problem for rational matrix functions on the real line

From the mid-1980s R.L. Ellis, I. Gohberg and D.C. Lay wrote several papers on systems of orthogonal matrix polynomials and matrix functions, culminating in the monograph [3] by Ellis and Gohberg, where additional background and further references can be found. Inverse problems related to these orthogonal systems were first considered in [2] for scalar-valued Wiener functions on the circle, both for unilateral systems (onefold problem) and bilateral systems (twofold problem). In later work extensions of the onefold inverse problem on the circle were considered for square matrix-valued polynomials in [5] and for square matrix-valued Wiener functions in [4]. Nonsquare versions were only recently dealt with in [12] and [13] for the onefold problems on the circle and real line, respectively, while nonsquare twofold problems on the circle and real line were solved in [9] and [10], respectively. In this paper we further develop the solution to the twofold inverse problem on the..

Closely connected unitary realizations of the solutions to the basic interpolation problem for generalized Schur functions

A generalized Schur function which is holomorphic at z = 0 can be written as the characteristic function of a closely connected unitary colligation with a Pontryagin state space. We describe the closely connected unitary colligation of a solution s(z) of the basic interpolation problem for generalized Schur functions (studied in [3]) in terms of the interpolation data and the canonical unitary colligation of the parameter function s(1)(z) appearing in the formula for s(z). In particular, we consider the case where the interpolation data and the Taylor coefficients of s(1)(z) at z = 0 are real. We also show that the canonical unitary colligation of s(1)(z) can be recovered from that of s(z)

A State Space Approach to Canonical Factorization with Applications

The present book deals with canonical factorization of matrix and operator functions that appear in state space form or that can be transformed into such a form. A unified geometric approach is used. The main results are all expressed explicitly in terms of matrices or operators, which are parameters of the state space representation. The applications concern different classes of convolution equations. A large part the book deals with rational matrix functions only

Group Communication In Amoeba And Its Applications

Unlike many other operating systems, Amoeba is a distributed operating system that provides group communication (i.e., one-to-many communication). We will discuss design issues for group communication, Amoeba's group system calls, and the protocols to implement group communication. To demonstrate that group communication is a useful abstraction, we will describe a design and implementation of a fault-tolerant directory service. We discuss two versions of the directory service: one with Non-Volatile RAM (NVRAM) and one without NVRAM. We will give performance figures for both implementations. 1. Introduction Most current distributed operating systems provide only Remote Procedure Call (RPC) [6]. The idea is to hide the message passing, and make the communication look like an ordinary procedure call (see Figure 1). The sender, called the client , calls a stub routine on its own machine that builds a message containing the name of the procedure to be called and all the parameters. It the..