Research Article
The Gershgorin Type Theorem on Localization of the Eigenvalues of Infinite Matrices and Zeros of Entire Functions
Abstract
The classical Gershgorin theorem on localization of the eigenvalues of finite matrices is extended to infinite Hille-Tamarkin matrices. Applications to finite order entire functions
are also discussed.
References
- Da Fonseca, C. M. On the location of the eigenvalues of Jacobi matrices. Appl. Math. Lett. 19 , no. 11, (2006) 1168-–1174.
- Reference1\bibitem{Dewan} Dewan, K.K., Govil, N.K. On the location of the zeros of analytic functions. Int. J. Math. Math. Sci. 13(1), (1990) 67-–72.
- Djordjevi\'c, S. V. and Kant\`un-Montiel, G. Localization and computation in an approximation of eigenvalues. Filomat 29 (2015), no. 1, 75–-81.
- Dyakonov, K.M. Polynomials and entire functions: zeros and geometry of the unit ball. Math. Res. Lett. 7(4), (2000) 393-–404.
- Esp\`inola-Rocha, J. A. Factorization of the scattering matrix and the location of the eigenvalues of the Manakov-Zakharov-Shabat system. Phys. Lett. A 372, no. 40, (2008) 6161-–6167.
- Gil’, M.I. Invertibility and spectrum of Hille-Tamarkin matrices, Mathematische Nachrichten , 244, (2002), 1-11
- Gil’, M.I.: Operator Functions and Localization of Spectra. Lectures Notes in Mathematics, vol. 1830, Springer, 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.
- Grammont, L. and Largillier, A. Krylov method revisited with an application to the localization of eigenvalues. Numer. Funct. Anal. Optim. 27 (2006), no. 5-6, 583-–618.
- Ioakimidis, N.I. A unified Riemann–-Hilbert approach to the analytical determination of zeros of sectionally analytic functions. J. Math. Anal. Appl. 129(1), (1988) 134–-141
- Kato, T., Perturbation Theory for Linear Operators, Berlin: Springer-Verlag, 1980.
- Kytmanov A.M. and Khodos O.V., On localization of zeros of an entire function of finite order of growth, Complex Anal. Oper. Theory 11 (2017) 393-–416.
Year 2022,
Volume: 4 Issue: 1, 9 - 16, 23.09.2022
Abstract
References
- Da Fonseca, C. M. On the location of the eigenvalues of Jacobi matrices. Appl. Math. Lett. 19 , no. 11, (2006) 1168-–1174.
- Reference1\bibitem{Dewan} Dewan, K.K., Govil, N.K. On the location of the zeros of analytic functions. Int. J. Math. Math. Sci. 13(1), (1990) 67-–72.
- Djordjevi\'c, S. V. and Kant\`un-Montiel, G. Localization and computation in an approximation of eigenvalues. Filomat 29 (2015), no. 1, 75–-81.
- Dyakonov, K.M. Polynomials and entire functions: zeros and geometry of the unit ball. Math. Res. Lett. 7(4), (2000) 393-–404.
- Esp\`inola-Rocha, J. A. Factorization of the scattering matrix and the location of the eigenvalues of the Manakov-Zakharov-Shabat system. Phys. Lett. A 372, no. 40, (2008) 6161-–6167.
- Gil’, M.I. Invertibility and spectrum of Hille-Tamarkin matrices, Mathematische Nachrichten , 244, (2002), 1-11
- Gil’, M.I.: Operator Functions and Localization of Spectra. Lectures Notes in Mathematics, vol. 1830, Springer, 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.
- Grammont, L. and Largillier, A. Krylov method revisited with an application to the localization of eigenvalues. Numer. Funct. Anal. Optim. 27 (2006), no. 5-6, 583-–618.
- Ioakimidis, N.I. A unified Riemann–-Hilbert approach to the analytical determination of zeros of sectionally analytic functions. J. Math. Anal. Appl. 129(1), (1988) 134–-141
- Kato, T., Perturbation Theory for Linear Operators, Berlin: Springer-Verlag, 1980.
- Kytmanov A.M. and Khodos O.V., On localization of zeros of an entire function of finite order of growth, Complex Anal. Oper. Theory 11 (2017) 393-–416.
There are 12 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Early Pub Date | March 10, 2022 |
| Publication Date | September 23, 2022 |
| Acceptance Date | March 3, 2022 |
| Published in Issue | Year 2022 Volume: 4 Issue: 1 |
