- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Journal of Complex Analysis
Volume 2013 (2013), Article ID 801382, 5 pages
Perturbations of Polynomials with Operator Coefficients
Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, 84105 Beer-Sheva, Israel
Received 18 December 2012; Accepted 20 February 2013
Academic Editor: Janne Heittokangas
Copyright © 2013 Michael Gil'. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- L. Rodman, An Introduction to Operator Polynomials, vol. 38 of Operator Theory: Advances and Applications, Birkhäuser, Basel, Switzerland, 1989.
- E. Bairamov, Ö. Çakar, and A. M. Krall, “Spectral properties, including spectral singularities, of a quadratic pencil of Schrödinger operators on the whole real axis,” Quaestiones Mathematicae, vol. 26, no. 1, pp. 15–30, 2003.
- P. A. Cojuhari, “Estimates of the discrete spectrum of a linear operator pencil,” Journal of Mathematical Analysis and Applications, vol. 326, no. 2, pp. 1394–1409, 2007.
- R. F. Efendiev, “Spectral analysis for one class of second-order indefinite non-self-adjoint differential operator pencil,” Applicable Analysis, vol. 90, no. 12, pp. 1837–1849, 2011.
- M. I. Gil', “On bounds for spectra of operator pencils in a Hilbert space,” Acta Mathematica Sinica (English Series), vol. 19, no. 2, pp. 313–326, 2003.
- M. I. Gil', “Bounds for the spectrum of analytic quasinormal operator pencils,” Communications in Contemporary Mathematics, vol. 5, no. 1, pp. 101–118, 2003.
- M. I. Gil', “Sums of characteristic values of compact polynomial operator pencils,” Journal of Mathematical Analysis and Applications, vol. 338, no. 2, pp. 1469–1476, 2008.
- M. Hasanov, “An approximation method in the variational theory of the spectrum of operator pencils,” Acta Applicandae Mathematicae, vol. 71, no. 2, pp. 117–126, 2002.
- I. V. Kurbatova, “A Banach algebra associated with a linear operator pencil,” Matematicheskie Zametki, vol. 86, no. 3, pp. 394–401, 2009 (Russian), translation in Mathematical Notes, vol. 86 (2009), no. 3-4, 361–367.
- I. V. Kurbatova, “A functional calculus generated by a quadratic operator pencil,” Journal of Mathematical Sciences, vol. 182, no. 5, pp. 646–655, 2012.
- M. D. Manafov and A. Kablan, “On a quadratic pencil of differential operators with periodic generalized potential,” International Journal of Pure and Applied Mathematics, vol. 50, no. 4, pp. 515–522, 2009.
- Y. Yakubov, “Fold completeness of a system of root vectors of a system of unbounded polynomial operator pencils in Banach spaces. I. Abstract theory,” Journal de Mathématiques Pures et Appliquées, vol. 92, no. 3, pp. 263–275, 2009.
- M. I. Gil', Difference Equations in Normed Spaces: Stability and Oscillations, vol. 206 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, The Netherlands, 2007.
- M. I. Gil', Operator Functions and Localization of Spectra, vol. 1830 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2003.