## Über Stabilität und asymptotisches Verhalten der Lösungen eines Systems endlicher Differenzengleichungen.

Published in Journal für die reine und angewandte Mathematik (Crelles Journal)

Published in Journal für die reine und angewandte Mathematik (Crelles Journal)

Published in Integral Equations and Operator Theory

In this paper, a function-theoretic approach to the completely indeterminate matricial Nehari Problem is given. The uniqueA-normalized resolvent matrixU is constructed by a limit procedure. Moreover, some limit relations for the Potapov-Ginzburg transform ofU are obtained.

Published in Integral Equations and Operator Theory

A time-variant version of the maximum principle for the central solution in the commutant lifting theorem is given. The main result is illustrated on the Parrott completion problem.

Published in Integral Equations and Operator Theory

Lagrange's interpolation formula is generalized to tangential interpolation. This includes interpolation by vector polynomials and by rational vector functions with prescribed pole characteristics. The formula is applied to obtain representations of the inverses of Cauchy-Vandermonde matrices generalizing former results.

Published in Integral Equations and Operator Theory

Nylen and Rodman [NR] introduced the notion of spectral radius property in Banach algebras in order to generalize a classical theorem of Yamamoto on the asymptotic behaviour of the singular values of ann xn matrix. In this paper we prove a conjecture of theirs in the affirmative, namely that any unital Banach algebra has the spectral radius propert...

Published in Integral Equations and Operator Theory

A boundary integral equations of the second kind in the logarithmic potential theory are studied under the assumption that the contour has a peak. For each equation we find a pair of function spaces such that the corresponding operator map one of them onto another. We describe also the kernels of the operators and find a condition for the trivialit...

Published in Integral Equations and Operator Theory

“Inversion formulas are obtained for a certain class of infinite matrices that possess displacement structure similar to that of finite block Toeplitz matrices. Consequences are symmetric inversion formulas for matrix-valued singular integral operators and infinite Toeplitz plus Hankel matrices”.

Published in Integral Equations and Operator Theory

We study the following problem: Given a Hilbert spaceH and a set of orthogonal projectionsP, Q1, ..., Qn on it, with the conditionsQj·Qk=δj,kQk,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-...

Published in Integral Equations and Operator Theory

LetM be a von Neumann algebra with a faithful normal tracial state τ and letH∞ be a finite maximal subdiagonal subalgebra ofM. LetH2 be the closure ofH∞ in the noncommutative Lebesgue spaceL2(M). We consider Toeplitz operators onH2 whose symbol belong toM, and find that they possess several of the properties of Toeplitz operators onH2(\documentclas...

Published in Integral Equations and Operator Theory

Three basic extension problems which were initiated by M. G. Krein are discussed and further developed. Connections with interpolation problems in the Carathéodory class are explained. Some tangential and bitangential versions are considered. Full characterizations of the classes of resolvent matrices for these problems are given and formulas for t...