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2012 | 66 | 1 |
Tytuł artykułu

Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space

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EN
Abstrakty
EN
We consider a second order regular differential operator whose coefficients are nonselfadjoint bounded operators acting in a Hilbert space. An estimate for the resolvent and a bound for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established.
Rocznik
Tom
66
Numer
1
Opis fizyczny
Daty
wydano
2012
online
2016-07-24
Twórcy
Bibliografia
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  • Baksi, O., Sezer, Y. and Karayel, S., The sum of subtraction of the eigenvalues of two selfadjoint differential operators with unbounded operator coefficient, Int. J. Pure Appl. Math. 63 (2010), no. 3, 255-268.
  • Gul, E., A regularized trace formula for a differential operator of second order with unbounded operator coefficients given in a finite interval, Int. J. Pure Appl. Math. 32 (2006), no. 2, 225-244.
  • Daleckii, Yu L., Krein, M. G., Stability of Solutions of Differential Equations in Banach Space, Translations of Mathematical Monographs, vol. 43, American Mathematical Society, Providence, R. I., 1974.
  • Gil’, M. I., Operator Functions and Localization of Spectra, Lecture Notes in Mathematics, vol. 1830, Springer-Verlag, Berlin, 2003.
  • Gil’, M. I., Localization and Perturbation of Zeros of Entire Functions, Lecture Notes in Pure and Applied Mathematics, 258, CRC Press, Boca Raton, FL, 2010.
  • Gil’, M. I., Bounds for the spectrum of a matrix differential operator with a damping term, Z. Angew. Math. Phys. 62 (2011), no. 1, 87-97.
  • Gohberg, I. C., Krein, M. G., Introduction to the Theory of Linear Nonselfadjoint Operators, Translations of Mathematical Monographs, vol. 18, American Mathematical Society, Providence, R.I., 1969.
  • Gohberg, I. C., Krein, M. G., Theory and Applications of Volterra Operators in Hilbert Space, Translations of Mathematical Monographs, vol. 24, American Mathematical Society, R. I., 1970.
  • Krein, S. G., Linear Differential Equations in Banach Space, Translations of Mathematical Monographs, vol. 29, American Mathematical Society, Providence, R.I., 1971.
  • Kunstmann, P. C., Weis, L., Maximal Lp-regularity for parabolic equations, Fourier multiplier and H1-functional calculus, in: Functional Analytic Methods for Evolution Equations, Lecture Notes in Mathematics, vol. 1855, Springer, Berlin, 2004, 65-311.
  • Rofe-Beketov, F. S., Kholkin, A. M., Spectral Analysis of Differential Operators. Interplay between spectral and oscillatory properties, World Scientific Monograph Series in Mathematics, 7, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005.
  • Yakubov, S., Yakubov, Ya., Differential-Operator Equations. Ordinary and Partial Differential Equations, Chapman and Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, 103, Chapman & Hall/CRC, Boca Raton, FL, 2000.
Typ dokumentu
Bibliografia
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bwmeta1.element.ojs-doi-10_17951_a_2012_66_1_25-39
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