Stable factorization of operator polynomials. I: Spectral divisors simply behaved at infinity

DOI10.1016/0022-247X(80)90137-7zbMath0447.47009OpenAlexW1984217526MaRDI QIDQ1146364

Leonid Lerer, Israel Gohberg, Leiba Rodman

Publication date: 1980

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(80)90137-7

zbMATH Keywords

Wiener-Hopf factorizationFredholm indexoperator polynomials

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) (Semi-) Fredholm operators; index theories (47A53) Convolution, factorization for one variable harmonic analysis (42A85) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10)

Related Items

Explicit and asymptotic formulas for \(LDM^ t\) factorization of banded Toeplitz matrices, General theory of regular matrix polynomials and band Toeplitz operators, Extensions of matrix valued functions with rational polynomial inverses, Similarity of operator blocks and canonical forms. I. General results, feedback equivalence and Kronecker indices, Stable factorization of operator polynomials. II: Main results and applications to Toeplitz operators, Wiener-Hopf factorization of operator polynomials, Analytic operator functions with compact spectrum. I. Spectral nodes, linearization and equivalence, On an extension problem, generalized Fourier analysis, and an entropy formula, Analytic operator functions with compact spectrum. II. Spectral pairs and factorization, Analytic matrix functions with prescribed local data, On non-square sections of Wiener-Hopf operators, On analytic equivalence of operator polynomials, The Bezoutian and the eigenvalue-separation problem for matrix polynomials, Wiener-Hopf factorization of piecewise matrix polynomials

Cites Work

• Spectral analysis of matrix polynomials. I. Canonical forms and divisors
• On canonical factorization of operator polynomials, spectral divisors and Toeplitz matrices
• Spectral analysis of matrix polynomials. II. The resolvent form and spectral divisors
• On spectral analysis of non-monic matrix and operator polynomials. I: reduction to monic polynomials
• Spectral analysis of families of operator polynomials and a generalized Vandermonde matrix II: The infinite dimensional case
• Representations and Divisibility of Operator Polynomials
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item