Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 50 Sayı: 2, 433 - 443, 11.04.2021
https://doi.org/10.15672/hujms.701108

Öz

Kaynakça

  • [1] F. Abdmouleh, A. Ammar and A. Jeribi, Characterization of the pseudo-browder es- sential spectra of linear operators and application to a transport equation, J. Comput. Theor. Transp. 44 (3), 141-153, 2015.
  • [2] N. Dunford and J.T. Schwartz, Linear operators II, Interscience, 1963.
  • [3] K. Gustafson and J. Weidmann, On the essential spectrum, J. Math. Anal. Appl. 25, 121-127, 1969.
  • [4] A. Jeribi, Spectral Theory and Applications of Linear Operators and Block Operator Matrices, Springer-Verlag, 2015.
  • [5] A. Jeribi, Linear Operators and Their Essential Pseudospectra, Apple Academic Press, 2018.
  • [6] Z.I. Ismailov, Multipoint normal differential operators for first order, Opuscula Math. 29 (4), 399–414, 2009.
  • [7] Z.I. Ismailov, L. Cona and E. Otkun Çevik, Gelfand numbers of diagonal matrices, Hacet. J. Math. Stat. 44 (1), 75-81, 2015.
  • [8] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, 1980.
  • [9] A.N. Kochubei, Symmetric operators and nonclassical spectral problems, Mat. Za- metki. 25 (3), 425–434, 1979.
  • [10] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Sequence Spaces, Springer-Verlag, 1977.
  • [11] R. Mennicken and A.K. Motovilov, Operator interpretation of resonances arising in spectral problems for 2 × 2 operator matrices, Math. Nachr. 201, 117-181, 1999.
  • [12] E. Otkun Çevik and Z.I. Ismailov, Spectrum of the direct sum of operators, Electron. J. Differential Equations, 210, 1–8, 2012.
  • [13] M. Schechter, On the essential spectrum of an arbitrary operator, I. J. Math. Anal. Appl. 13, 205-215, 1966.
  • [14] S. Timoshenko, Theory of Elastic Stability, McGraw-Hill Book Co, 1961.
  • [15] C. Tretter, Spectral Theory of Block Operator Matrices and Applications, Imperial College Press, 2008.
  • [16] H. Weyl, Uber beschrankte quadratische Formen, deren differenz vollstelig ist, Rend. Circ. Mat. Palermo, 27, 373-392, 1909.
  • [17] A. Zettl, Sturm-Lioville Theory, Mathematical Surveys and Monographs, American Mathematical Society, 2005.

$S$-spectra and $S$-essential pseudospectra of the diagonal block operator matrices

Yıl 2021, Cilt: 50 Sayı: 2, 433 - 443, 11.04.2021
https://doi.org/10.15672/hujms.701108

Öz

In this article, the relationships between the $S$-spectra, the $ S$-spectral radius, the $ \epsilon$-$S$-essential pseudospectra, and the $ \epsilon$-$S$-essential pseudospectral radius of the diagonal block operator matrices in the direct sum of Banach spaces and their block coordinate operators are studied. Then, the results are supported by applications.

Kaynakça

  • [1] F. Abdmouleh, A. Ammar and A. Jeribi, Characterization of the pseudo-browder es- sential spectra of linear operators and application to a transport equation, J. Comput. Theor. Transp. 44 (3), 141-153, 2015.
  • [2] N. Dunford and J.T. Schwartz, Linear operators II, Interscience, 1963.
  • [3] K. Gustafson and J. Weidmann, On the essential spectrum, J. Math. Anal. Appl. 25, 121-127, 1969.
  • [4] A. Jeribi, Spectral Theory and Applications of Linear Operators and Block Operator Matrices, Springer-Verlag, 2015.
  • [5] A. Jeribi, Linear Operators and Their Essential Pseudospectra, Apple Academic Press, 2018.
  • [6] Z.I. Ismailov, Multipoint normal differential operators for first order, Opuscula Math. 29 (4), 399–414, 2009.
  • [7] Z.I. Ismailov, L. Cona and E. Otkun Çevik, Gelfand numbers of diagonal matrices, Hacet. J. Math. Stat. 44 (1), 75-81, 2015.
  • [8] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, 1980.
  • [9] A.N. Kochubei, Symmetric operators and nonclassical spectral problems, Mat. Za- metki. 25 (3), 425–434, 1979.
  • [10] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Sequence Spaces, Springer-Verlag, 1977.
  • [11] R. Mennicken and A.K. Motovilov, Operator interpretation of resonances arising in spectral problems for 2 × 2 operator matrices, Math. Nachr. 201, 117-181, 1999.
  • [12] E. Otkun Çevik and Z.I. Ismailov, Spectrum of the direct sum of operators, Electron. J. Differential Equations, 210, 1–8, 2012.
  • [13] M. Schechter, On the essential spectrum of an arbitrary operator, I. J. Math. Anal. Appl. 13, 205-215, 1966.
  • [14] S. Timoshenko, Theory of Elastic Stability, McGraw-Hill Book Co, 1961.
  • [15] C. Tretter, Spectral Theory of Block Operator Matrices and Applications, Imperial College Press, 2008.
  • [16] H. Weyl, Uber beschrankte quadratische Formen, deren differenz vollstelig ist, Rend. Circ. Mat. Palermo, 27, 373-392, 1909.
  • [17] A. Zettl, Sturm-Lioville Theory, Mathematical Surveys and Monographs, American Mathematical Society, 2005.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Pembe Ipek Al 0000-0002-6111-1121

Zameddin İsmailov 0000-0001-5193-5349

Yayımlanma Tarihi 11 Nisan 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 50 Sayı: 2

Kaynak Göster

APA Ipek Al, P., & İsmailov, Z. (2021). $S$-spectra and $S$-essential pseudospectra of the diagonal block operator matrices. Hacettepe Journal of Mathematics and Statistics, 50(2), 433-443. https://doi.org/10.15672/hujms.701108
AMA Ipek Al P, İsmailov Z. $S$-spectra and $S$-essential pseudospectra of the diagonal block operator matrices. Hacettepe Journal of Mathematics and Statistics. Nisan 2021;50(2):433-443. doi:10.15672/hujms.701108
Chicago Ipek Al, Pembe, ve Zameddin İsmailov. “$S$-Spectra and $S$-Essential Pseudospectra of the Diagonal Block Operator Matrices”. Hacettepe Journal of Mathematics and Statistics 50, sy. 2 (Nisan 2021): 433-43. https://doi.org/10.15672/hujms.701108.
EndNote Ipek Al P, İsmailov Z (01 Nisan 2021) $S$-spectra and $S$-essential pseudospectra of the diagonal block operator matrices. Hacettepe Journal of Mathematics and Statistics 50 2 433–443.
IEEE P. Ipek Al ve Z. İsmailov, “$S$-spectra and $S$-essential pseudospectra of the diagonal block operator matrices”, Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 2, ss. 433–443, 2021, doi: 10.15672/hujms.701108.
ISNAD Ipek Al, Pembe - İsmailov, Zameddin. “$S$-Spectra and $S$-Essential Pseudospectra of the Diagonal Block Operator Matrices”. Hacettepe Journal of Mathematics and Statistics 50/2 (Nisan 2021), 433-443. https://doi.org/10.15672/hujms.701108.
JAMA Ipek Al P, İsmailov Z. $S$-spectra and $S$-essential pseudospectra of the diagonal block operator matrices. Hacettepe Journal of Mathematics and Statistics. 2021;50:433–443.
MLA Ipek Al, Pembe ve Zameddin İsmailov. “$S$-Spectra and $S$-Essential Pseudospectra of the Diagonal Block Operator Matrices”. Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 2, 2021, ss. 433-4, doi:10.15672/hujms.701108.
Vancouver Ipek Al P, İsmailov Z. $S$-spectra and $S$-essential pseudospectra of the diagonal block operator matrices. Hacettepe Journal of Mathematics and Statistics. 2021;50(2):433-4.