Spectral analysis of families of operator polynomials and a generalized Vandermonde matrix II: The infinite dimensional case

DOI10.1016/0022-1236(78)90063-0zbMath0404.47011OpenAlexW1979318092MaRDI QIDQ1256708

Israel Gohberg, Leiba Rodman, Marinus A. Kaashoek

Publication date: 1978

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(78)90063-0

zbMATH Keywords

Generalized InverseGeneralized Vandermonde Operator MatrixMonic PolynomialsRight Divisors

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) Structure theory of linear operators (47A65) General theory of linear operators (47A99)

Related Items

Common multiples and common divisors of matrix polynomials, II. Vandermonde and resultant matrices, A block bidiagonal form for block companion matrices, Bezout equation, Vandermonde operators, and common multiples for operator polynomials, Algebraic and differential operator equations, Divisors of operator functions, holomorphic in a bounded, simply connected domain, Stable factorization of operator polynomials. I: Spectral divisors simply behaved at infinity, Stable factorization of operator polynomials. II: Main results and applications to Toeplitz operators, Analytic operator functions with compact spectrum. II. Spectral pairs and factorization, Common eigenvalues, divisors, and multiples of matrix polynomials: A review, Common multiples of operator polynomials with analytic coefficients, On existence of common multiples of monic operator polynomials, Some criteria for the existence of divisors of a holomorphic operator function, Factorization of determinants over finite fields and application in stream ciphers

Cites Work

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• Spectral analysis of matrix polynomials. I. Canonical forms and divisors
• Spectral analysis of matrix polynomials. II. The resolvent form and spectral divisors
• On some mathematical principles in the linear theory of damped oscillations of continua II
• ON THE COMPLETEn-TUPLE OF ROOTS OF THE OPERATOR EQUATION CORRESPONDING TO A POLYNOMIAL OPERATOR BUNDLE
• The Algebraic Theory of Matrix Polynomials
• Approximate Proper Vectors