Some description of essential structured approximate and defect pseudospectrum
Main Article Content
Abstract
In this paper, we introduce and study the structured essential approximate and defect pseudospectrum of closed, densely defined linear operators in a Banach space. Beside that, we discuss some results of stability and some properties of these essential pseudospectra. Finally, we will apply the results described above to investigate the essential approximate and defect pseudospectra of the following integro-differential transport operator.
Article Details
References
[1] A. Ammar and A. Jeribi, A characterization of the essential pseudospectra and application to a transport equation, Extra Math. 28 (2013), 95–112. Google Scholar
[2] A. Ammar, A. Jeribi and K. Mahfoudhi, A characterization of the essential approximation pseudospectrum on a Banach space, Filomath 31 (11) (2017), 3599–3610. Google Scholar
[3] 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. Google Scholar
[4] E. B. Davies, Linear Operators and their spectra, Cambridge Studies in Advanced Mathematics, 106. Camb. Univ. Press, Cambridge (2007). Google Scholar
[5] A. Jeribi, Time asymptotic behavior for unbounded linear operator arising in growing cell populations, Nonli. Anal. Real World Appl. 4 2003 , 667–688. Google Scholar
[6] A. Jeribi, Fredholm operators and essential spectra, Arch. Ineq. Appl. 358 (2004) , 123–140. Google Scholar
[7] A. Jeribi, Spectral theory and applications of linear operators and block operator matrices, Springer-Verlag, New-York, (2015). Google Scholar
[8] 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. Google Scholar
[9] V. Mu ̈ller, Spectral theory of linear operators and spectral system in Banach algebras, Oper. Theor. Adv. Appl. 139 (2003). Google Scholar
[10] M. Schechter, Principles of functional analysis, Second edition. Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 36 (2002). Google Scholar
[11] M. Schechter, Spectra of partial differential operators, North-Holland, Amsterdam, New-York (1986). Google Scholar
[12] L. N. Trefethen, Pseudospectra of matrices. numerical analysis, In Pitman Research notes in Mathematics Series, Longman Science and Technology, Harlow 260 (1992), 234–266. Google Scholar
[13] L. N. Trefethen, Pseudospectra of linear operators, SAIM rev. 39 (3) 383-406, (1997). Google Scholar
[14] M. P. H. Wolff, Discrete approximation of unbounded operators and approximation of their spectra, J. Approx. Theo. 113 (2001), 229–244. Google Scholar
[15] E. Shargorodsky, On the definition of pseudospectra, Bull. London Math. Soc. 41 (2009) 524–534. Google Scholar