Showing papers by "Israel Gohberg published in 1996"
01 Jan 1996
TL;DR: In this article, all irreducible representations of Banach algebras generated by N idempotents which satisfy some additional relations are described and constructed a symbol theory with applications to singular integral operators.
Abstract: It is well known that for Banach algebras generated by two idempotents and the identity all irreducible representations are of order not greater than two. These representations have been described completely and have found important applications to symbol theory. It is also well known that without additional restrictions on the idempotents these results do not admit a natural generalization to algebras generated by more than two idempotents and the identity. In this paper we describe all irreducible representations of Banach algebras generated by N idempotents which satisfy some additional relations. These representations are of order not greater than N and allow us to construct a symbol theory with applications to singular integral operators.
27 citations
TL;DR: In this article, the problem of classifying linear time-varying finite dimensional systems of difference equations under kinematic similarity was studied, i.e., under a uniformly bounded change of variables of which the inverse is also uniformly bounded.
Abstract: This paper concerns the problem to classify linear time-varying finite dimensional systems of difference equations under kinematic similarity, i.e., under a uniformly bounded time-varying change of variables of which the inverse is also uniformly bounded. Also the problem of reducing difference equations by using such similarity transformations is studied. Both problems are solved for a number of subclasses, including equations with scalar coefficients, time-invariant equations, finitely supported equations, and equations with one jump. For the general case an open problem is formulated.
22 citations
TL;DR: In this paper, necessary and sufficient conditions for the existence of solutions to discrete time-variant interpolation problems of Nevanlinna-Pick and Nudelman type were derived.
Abstract: Necessary and sufficient conditions are derived for the existence of solutions to discrete time-variant interpolation problems of Nevanlinna-Pick and Nudelman type. The proofs are based on a reduction scheme which allows one to treat these time-variant interpolation problems as classical interpolation problems for operator-valued functions with operator arguments. The latter ones are solved by using the commutant lifting theorem.
17 citations
TL;DR: Explicit formulas for triangular factors of Cauchy and Vandermonde matrices and their inverses in terms of entries of these matrices are presented in this article, where they are shown to be invertible.
Abstract: Explicit formulas for triangular factors of Cauchy and Vandermonde matrices and their inverses in terms of entries of these matrices are presented.
16 citations
01 Jan 1996
TL;DR: In this article, an explicit formula for the reflexivity coefficient function (or potential) of an ordinary differential operator if its reflection coefficient is a rational matrix valued function is given in terms of a realization of the reflection coefficient function.
Abstract: In this paper we obtain explicit formula for the reflexivity coefficient function (or potential) of an ordinary differential operator if its reflection coefficient is a rational matrix valued function. The solution is given in terms of a realization of the reflection coefficient function.
12 citations
01 Jan 1996
TL;DR: In this article, the Grassmannian approach is used to develop a new addition of the band method, which allows one to obtain a linear fractional representation of all solutions of a completion problem from special extensions that are not necessarily band extensions.
Abstract: The Grassmannian approach is used to develop a new addition of the band method. This addition allows one to obtain a linear fractional representation of all solutions of a completion problem from special extensions that are not necessarily band extensions (for the positive case) or triangular extensions (for the contractive case). Also linear fractional representations are obtained for all solutions of a completion problem of non-band type.
11 citations
TL;DR: In this article, the solutions of the two extension problems mentioned in the title are described via linear fractional transformations, and the coefficient matrix functions of these transformations are related to each other.
Abstract: The solutions of the two extension problems mentioned in the title are described via linear fractional transformations. In this paper, we relate the coefficient matrix functions of these transformations.
7 citations
TL;DR: A class of matrices, each of which is the sum of an identity matrix and a self-adjoint block Toeplitz matrix that has a symmetric band of zero blocks is considered.
6 citations
TL;DR: In this article, the authors considered the problem of canonical factorization of a rational matrix function W(ψ) which is analytic but may be invertible at infinity, where the factors are obtained explicitly in terms of the realization of the original matrix function.
Abstract: This paper concerns the problem of canonical factorization of a rational matrix functionW(ψ) which is analytic but may benot invertible at infinity. The factors are obtained explicitly in terms of the realization of the original matrix function. The cases of symmetric factorization for selfadjoint and positive rational matrix functions are considered separately.
01 Jan 1996
TL;DR: In this paper, the authors prove continuous analogues of results concerning the distribution of zeros of orthogonal matrix functions related to the Nehari problem in the context of matrix functions.
Abstract: In this paper, we prove continuous analogues of results concerning the distribution of zeros of orthogonal matrix functions related to the Nehari problem.
TL;DR: In this article, the notions of norm and spectral radius of a matrix were generalized to spaces with an indefinite metric and a spectral radius formula was established, which is the basis for the present paper.
Abstract: The notions of norm and spectral radius of a matrix are generalized to spaces with an indefinite metric. A spectral radius formula is established.
TL;DR: In this paper, the behavior of singular values s k ( A n ), k = 1, 2, …, r, of the n th power of an r × r matrix A is analyzed for n → ∞.
TL;DR: In this paper, the usual power method for matrices is generalized for contractions in indefinite metric spaces, and this generalization unifies the power method and the inertia theorem in a natural way.
TL;DR: In this paper, it was shown that a lower triangular strictly m-banded infinite matrix can be factored into a product of m lower triangular 1-bandsed matrices, and a method to construct such a factorization was described.