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

Michael Gil’

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2012)

  • Volume: 66, Issue: 1
  • ISSN: 0365-1029

Abstract

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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.

How to cite

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Michael Gil’. "Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 66.1 (2012): null. <http://eudml.org/doc/289838>.

@article{MichaelGil2012,
abstract = {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.},
author = {Michael Gil’},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Abstract differential operator; spectrum; resolvent, stability; instability},
language = {eng},
number = {1},
pages = {null},
title = {Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space},
url = {http://eudml.org/doc/289838},
volume = {66},
year = {2012},
}

TY - JOUR
AU - Michael Gil’
TI - Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2012
VL - 66
IS - 1
SP - null
AB - 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.
LA - eng
KW - Abstract differential operator; spectrum; resolvent, stability; instability
UR - http://eudml.org/doc/289838
ER -

References

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  3. 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. 
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  8. 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. 
  9. 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. 
  10. 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. 
  11. Krein, S. G., Linear Differential Equations in Banach Space, Translations of Mathematical Monographs, vol. 29, American Mathematical Society, Providence, R.I., 1971. 
  12. 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. 
  13. 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. 
  14. 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. 

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