Acknowledgement
The authors would like to express their cordial gratitude to the referee for his/her kind comments.
References
- A. Ammar and A. Jeribi, A characterization of the essential pseudospectra and application to a transport equation, Extra Math. 28 (2013), 95-112.
- A. Ammar, A. Jeribi and K. Mahfoudhi, A characterization of the essential approximation pseudospectrum on a Banach space, Filomath 31 (11) (2017), 3599-3610. https://doi.org/10.2298/FIL1711599A
- A. Ammar, A. Jeribi and K. Mahfoudhi, Global Bifurcation from the real leading eigenvalue of the transport operator, Journal of Computational and Theoretical Transport 46 (2017), 229-241. https://doi.org/10.1080/23324309.2017.1336729
- E. B. Davies, Linear Operators and their spectra, Cambridge Studies in Advanced Mathematics, 106. Camb. Univ. Press, Cambridge (2007).
- A. Jeribi, Time asymptotic behavior for unbounded linear operator arising in growing cell populations, Nonli. Anal. Real World Appl. 4 2003 , 667-688. https://doi.org/10.1016/S1468-1218(02)00069-X
- A. Jeribi, Fredholm operators and essential spectra, Arch. Ineq. Appl. 358 (2004), 123-140.
- A. Jeribi, Spectral theory and applications of linear operators and block operator matrices, Springer-Verlag, New-York, (2015).
- A. Jeribi and N. Moalla, A characterization of some subsets of Schechter's essential spectrum and application to singular transport equation, J. Math. Anal. Appl. 358 (2009), 434-444. https://doi.org/10.1016/j.jmaa.2009.04.053
- V. Muller, Spectral theory of linear operators and spectral system in Banach algebras, Oper. Theor. Adv. Appl. 139 (2003).
- M. Schechter, Principles of functional analysis, Second edition. Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 36 (2002).
- M. Schechter, Spectra of partial differential operators, North-Holland, Amsterdam, New-York (1986).
- L. N. Trefethen, Pseudospectra of matrices. numerical analysis, In Pitman Research notes in Mathematics Series, Longman Science and Technology, Harlow 260 (1992), 234-266.
- L. N. Trefethen, Pseudospectra of linear operators, SAIM rev. 39 (3) 383-406, (1997).
- M. P. H. Wolff, Discrete approximation of unbounded operators and approximation of their spectra, J. Approx. Theo. 113 (2001), 229-244. https://doi.org/10.1006/jath.2001.3588
- E. Shargorodsky, On the definition of pseudospectra, Bull. London Math. Soc. 41 (2009) 524-534. https://doi.org/10.1112/blms/bdp031