Representations and Divisibility of Operator Polynomials

I. Gohberg; P. Lancaster; L. Rodman

doi:10.4153/CJM-1978-088-2

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let be a complex Banach space and the algebra of bounded linear operators on . In this paper we study functions from the complex numbers to of the form

References

1. Dunford, N. and Schwartz, J. T., Linear operators, Part I: General theory (Interscience Pub., New York, 1966).Google Scholar

2. Gohberg, I., Kaashoek, M., and Rodman, L., Spectral analysis of families of operator poly nomials and a generalized Vandermonde matrix, I., Advances in Mathematics, to appear.Google Scholar

3. Gohberg, I., Lancaster, P., and Rodman, L., Spectral analysis of matrix polynomials, I. Canonical forms and divisors, J. Lin. Alg. Applic. 20 (1978), 1–44.Google Scholar

4. Gohberg, I., Lancaster, P., and Rodman, L., Spectral analysis of matrix polynomials, II. The resolvent form and spectral divisors, J. Lin. Alg. Applic. 21 (1978), 65–88.Google Scholar

5. Lancaster, P., A fundamental theorem of lambda-matrices, /. Ordinary differential equations with constant coefficients, J. Lin. Alg. Applic. 18 (1977), 189–211.Google Scholar

6. Lancaster, P., A fundamental theorem on lambda-matrices II. Difference equations with constant coefficients. J. Lin. Alg. Applic. 18 (1977), 213–222.Google Scholar

7. Langer, H., Ùber eine Klasse nichtlinearer Eigenwertprobleme, Acta Sc. Math. 35 (1973), 73–86.Google Scholar

8. Langer, H., Factorization of operator pencils, Acta Sc. Math. 38 (1976), 83–96.Google Scholar

9. Markus, A. S. and Mereutsa, I. V., On the complete n-tuple of roots of the operator equation corresponding to a polynomial operator bundle, Izvestia Akad. Nauk. SSSR, Ser. Mat. 37 (1973) 1108–1131 (Russian). (English Transi., Math., USSR Izvestija 7 (1973), 1105- 1128.)Google Scholar

10. Mereutsa, I. V., On the properties of the roots of an operator equation corresponding to a polynomial operator pencil, Mat. Issled. Kishinev. (27), (1973), 96–115 (Russian).Google Scholar

11. Pattabhiraman, M. V. and Lancaster, P., Spectral properties of operator polynomials, Numer. Math. 13 (1969), 247–259.Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Thijsse, G. Philip A. 1978. On solutions of elliptic differential equations with operator coefficients. Integral Equations and Operator Theory, Vol. 1, Issue. 4, p. 567.

Gohberg, I. Lerer, L. and Rodman, L. 1978. On canonical factorization of operator polynomials, spectral divisors and toeplitz matrices. Integral Equations and Operator Theory, Vol. 1, Issue. 2, p. 176.

Gohberg, I. and Rodman, L. 1979. On the spectral structure of monic matrix polynomials and the extension problem. Linear Algebra and its Applications, Vol. 24, Issue. , p. 157.

Rodman, Leiba 1979. On analytic equivalence of operator polynomials. Integral Equations and Operator Theory, Vol. 2, Issue. 1, p. 48.

Gohberg, I. Lancaster, P. and Rodman, L. 1979. Perturbation Theory for Divisors of Operator Polynomials. SIAM Journal on Mathematical Analysis, Vol. 10, Issue. 6, p. 1161.

den Boer, H. and Thijsse, G. Ph. A. 1980. Semi-stability of sums of partial multiplicities under additive perturbation. Integral Equations and Operator Theory, Vol. 3, Issue. 1, p. 23.

Gohberg, I Lerer, L and Rodman, L 1980. Stable factorization of operator polynomials, I. Spectral divisors simply behaved at infinity. Journal of Mathematical Analysis and Applications, Vol. 74, Issue. 2, p. 401.

Gohberg, I Lerer, L and Rodman, L 1980. Stable factorization of operator polynomials. II. Main results and applications to Toeplitz operators. Journal of Mathematical Analysis and Applications, Vol. 75, Issue. 1, p. 1.

Kaashoek, M. A. van der Mee, C. V. M. and Rodman, L. 1981. Analytic operator functions with compact spectrum. I. Spectral nodes, linearization and equivalence. Integral Equations and Operator Theory, Vol. 4, Issue. 4, p. 504.

Lancaster, P. 1981. Minimal Factorization of Matrix and Operator Functions (H. Bart, I. Gohberg, and M. A. Kaashoek). SIAM Review, Vol. 23, Issue. 4, p. 551.

Wimmer, Harald K. 1981. The structure of nonsingular polynomial matrices. Mathematical Systems Theory, Vol. 14, Issue. 1, p. 367.

Kaashoek, M. A. van der Mee, C. V. M. and Rodman, L. 1982. Analytic operator functions with compact spectrum. II. Spectral pairs and factorization. Integral Equations and Operator Theory, Vol. 5, Issue. 1, p. 791.

Fuhrmann, Paul A. 1982. Feedback Control of Linear and Nonlinear Systems. Vol. 39, Issue. , p. 78.

Cohen, Nir 1983. Spectral analysis of regular matrix polynomials. Integral Equations and Operator Theory, Vol. 6, Issue. 1, p. 161.

Fuhrmann, Paul A. 1983. On symmetric rational transfer functions. Linear Algebra and its Applications, Vol. 50, Issue. , p. 167.

Takahashi, Katsutoshi 1983. On relative primeness of operator polynomials. Linear Algebra and its Applications, Vol. 50, Issue. , p. 521.

Cohen, Nir 1983. On minimal factorizations of rational matrix functions. Integral Equations and Operator Theory, Vol. 6, Issue. 1, p. 647.

Lerer, L Rodman, L and Tismenetsky, M 1984. Bezoutian and Schur-Cohn problem for operator polynomials. Journal of Mathematical Analysis and Applications, Vol. 103, Issue. 1, p. 83.

Ball, Joseph A. Gohberg, Israel and Rodman, Leiba 1990. Interpolation of Rational Matrix Functions. p. 40.

Ball, Joseph A. Gohberg, Israel and Rodman, Leiba 1990. Interpolation of Rational Matrix Functions. p. 213.

Download full list

Article contents

Representations and Divisibility of Operator Polynomials

Extract

References

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests