Bezout operators for analytic operator functions. I: A general concept of Bezout operator

DOI10.1007/BF01262991zbMath0824.47012MaRDI QIDQ1891846

Leonid Lerer, Iulian Haimovici

Publication date: 1 November 1995

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

zbMATH Keywords

Bezoutiananalytic operator functionsmatrix and operator polynomialsBezout operator

Mathematics Subject Classification ID

Operator-theoretic methods (93B28) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10)

Related Items

Inversion of structured operators, On a class of entire matrix function equations, \(J\)-pseudo-spectral and \(J\)-inner-pseudo-outer factorizations for matrix polynomials, Bézoutians of rational matrix functions, matrix equations and factorizations, Bézout and Hankel matrices associated with row reduced matrix polynomials, Barnett type formulas, Zero distribution of matrix polynomials, Operator Bezoutiant and roots of entire functions, concrete examples, Symmetric factorizations and localization of zeroes of rational matrix functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On symmetric rational transfer functions
• Algebraic methods for Toeplitz-like matrices and operators
• On the history of the Bézoutian and the resultant matrix
• Bezoutian and Schur-Cohn problem for operator polynomials
• Generalized Bezoutian and the inversion problem for block matrices, I. General scheme
• Generalized Bézoutian and matrix equations
• On the discriminant function of two commuting nonselfadjoint operators
• On an extension problem, generalized Fourier analysis, and an entropy formula
• An introduction to operator polynomials
• Spectrum separation and inertia for operator polynomials
• Operational Bezoutiant in the theory of separation of roots of entire functions
• Linearization of holomorphic operator functions. I
• On the Routh-Hurwitz-Fujiwara and the Schur-Cohn-Fujiwara theorems for the root-separation problem
• On the effective computation of the inertia of a non-hermitian matrix
• The Bezoutian and the eigenvalue-separation problem for matrix polynomials
• A Schur-Cohn theorem for matrix polynomials
• The Bezoutian and the algebraic Riccati equation
• The kernel of the bezoutian for operator Polynomials^∗
• Generalized Bezoutian and Sylvester matrices in multivariable linear control
• Результантная матрица и ее обобщения
• Greatest common divisor via generalized Sylvester and Bezout matrices
• On the Hermite-Fujiwara theorem in stability theory
• A Note on the Bezoutian Matrix
• Matrix equation, matrix polynomial and the number of zeros of a polynomial inside the unit circle