Araştırma Makalesi
The uniform convergence of Fourier series expansions of a Sturm-Liouville problem with boundary condition which contains the eigenparameter
Öz
This paper is devoted to investigating the uniform convergence conditions of Fourier series expansions of continuous functions in terms of eigenfunctions of a Sturm-Liouville problem with eigenparameter in one of the boundary conditions on a closed interval. Such problems are quite common in mathematical physics problems.
Anahtar Kelimeler
Eigenvalues eigenfunctions uniform convergence of spectral expansion.
Kaynakça
- Gulyaev, D. A., On the uniform convergence of spectral expansions for a spectral problem with boundary conditions of the third kind one of which contains the spectral parameter, Differential Equations, 47(10) (2011), 1520-1524.
- Gulyaev, D. A., On the convergence in $W_2^m$ of spectral expansions for a spectral problem with boundary conditions of the third kind one of which contains the spectral parameter, Differential Equations, 48(10) (2012), 1429-1432.
- Kapustin, N. Yu., On the uniform convergence of the Fourier series for a spectral problem with squared spectral parameter in a boundary condition, Differential Equations, 46(10) (2010), 1507-1510.
- Kapustin, N. Yu., On the uniform convergence in $ C^1 $ of Fourier series for a spectral problem with squared spectral parameter in a boundary condition, Differential Equations, 47(10) (2011), 1408-1413.
- Kapustin, N. Yu., On the spectral problem arising in the solution of a mixed problem for the heat equation with a mixed derivative in the boundary conditions, Differential Equations, 48(5) (2012), 701-706.
- Kapustin, N. Yu. and Moiseev, E. I., Convergence of spectral expansions for functions of the H\"{o}lder class for two problems with a spectral parameter in the boundary condition, Differential Equations, 36(8) (2000), 1182-1188.
- Kapustin, N. Yu. and Moiseev, E. I., A remark on the convergence problem for spectral expansions corresponding to a classical problem with spectral parameter in the boundary condition, Differential Equations, 37(12) (2001), 1677-1683.
- Kerimov, N. B. and Maris E. A., On the basis properties and convergence of expansions in terms of eigenfunctions for a spectral problem with a spectral parameter in the boundary condition, Proc. IMM of NAS, 40 (2014), 245-258.
- Kerimov, N. B. and Maris E. A., On the uniform convergence of the Fourier Series for one spectral problem with a spectral parameter in a boundary condition, Math. Methods Appl. Sci, 39(9) (2016), 2298-2309.
- Kerimov, N. B. and Maris E. A., On the uniform convergence of Fourier series expansions for Sturm-Liouville problems with a spectral parameter in the boundary conditions, Results in Mathematics, 73(3) (2018), 102.
- Koyunbakan, H., Solving the hyperbolic problem obtained by transmutation operator, Leading-Edge Research on Evolution Equations, (2008), 185-195.
- Koyunbakan, H., The inverse nodal problem for a differential operator with an eigenvalue in the boundary condition, Applied Mathematics Letters, 21(12) (2008), 1301-1305.
- Levitan, B. M. and Sargsjan, I. S., Sturm-Liouville and Dirac Operators, Kluwer Academic Publishers: Netherlands, 1991.
- Marchenkov, D. B., On the convergence of spectral expansions of functions for problems with a spectral parameter in a boundary condition, Differential Equations, 41(10) (2005), 1496-1500.
- Maris E. A. and Goktas, S., On the spectral properties of a Sturm-Liouville problem with eigenparameter in the boundary condition, HJMS, (2020), https://doi.org/10.15672/hujms.479445.
- Tikhonov, A. N. and Samarskii A. A., Equations of Mathematical Physics, New York, Courier Corporation, 2013; [in russian] Uravneniya Matematicheskoi Fiziki, Moscow, 1972.
- Wang, Y. P. and Koyunbakan, H., On the Hochstadt-Lieberman theorem for discontinuous boundary-valued problems, Acta Mathematica Sinica, English Series, 30(6) (2014), 985-992.
Yıl 2021,
Cilt: 70 Sayı: 1, 205 - 215, 30.06.2021
Öz
Kaynakça
- Gulyaev, D. A., On the uniform convergence of spectral expansions for a spectral problem with boundary conditions of the third kind one of which contains the spectral parameter, Differential Equations, 47(10) (2011), 1520-1524.
- Gulyaev, D. A., On the convergence in $W_2^m$ of spectral expansions for a spectral problem with boundary conditions of the third kind one of which contains the spectral parameter, Differential Equations, 48(10) (2012), 1429-1432.
- Kapustin, N. Yu., On the uniform convergence of the Fourier series for a spectral problem with squared spectral parameter in a boundary condition, Differential Equations, 46(10) (2010), 1507-1510.
- Kapustin, N. Yu., On the uniform convergence in $ C^1 $ of Fourier series for a spectral problem with squared spectral parameter in a boundary condition, Differential Equations, 47(10) (2011), 1408-1413.
- Kapustin, N. Yu., On the spectral problem arising in the solution of a mixed problem for the heat equation with a mixed derivative in the boundary conditions, Differential Equations, 48(5) (2012), 701-706.
- Kapustin, N. Yu. and Moiseev, E. I., Convergence of spectral expansions for functions of the H\"{o}lder class for two problems with a spectral parameter in the boundary condition, Differential Equations, 36(8) (2000), 1182-1188.
- Kapustin, N. Yu. and Moiseev, E. I., A remark on the convergence problem for spectral expansions corresponding to a classical problem with spectral parameter in the boundary condition, Differential Equations, 37(12) (2001), 1677-1683.
- Kerimov, N. B. and Maris E. A., On the basis properties and convergence of expansions in terms of eigenfunctions for a spectral problem with a spectral parameter in the boundary condition, Proc. IMM of NAS, 40 (2014), 245-258.
- Kerimov, N. B. and Maris E. A., On the uniform convergence of the Fourier Series for one spectral problem with a spectral parameter in a boundary condition, Math. Methods Appl. Sci, 39(9) (2016), 2298-2309.
- Kerimov, N. B. and Maris E. A., On the uniform convergence of Fourier series expansions for Sturm-Liouville problems with a spectral parameter in the boundary conditions, Results in Mathematics, 73(3) (2018), 102.
- Koyunbakan, H., Solving the hyperbolic problem obtained by transmutation operator, Leading-Edge Research on Evolution Equations, (2008), 185-195.
- Koyunbakan, H., The inverse nodal problem for a differential operator with an eigenvalue in the boundary condition, Applied Mathematics Letters, 21(12) (2008), 1301-1305.
- Levitan, B. M. and Sargsjan, I. S., Sturm-Liouville and Dirac Operators, Kluwer Academic Publishers: Netherlands, 1991.
- Marchenkov, D. B., On the convergence of spectral expansions of functions for problems with a spectral parameter in a boundary condition, Differential Equations, 41(10) (2005), 1496-1500.
- Maris E. A. and Goktas, S., On the spectral properties of a Sturm-Liouville problem with eigenparameter in the boundary condition, HJMS, (2020), https://doi.org/10.15672/hujms.479445.
- Tikhonov, A. N. and Samarskii A. A., Equations of Mathematical Physics, New York, Courier Corporation, 2013; [in russian] Uravneniya Matematicheskoi Fiziki, Moscow, 1972.
- Wang, Y. P. and Koyunbakan, H., On the Hochstadt-Lieberman theorem for discontinuous boundary-valued problems, Acta Mathematica Sinica, English Series, 30(6) (2014), 985-992.
Toplam 17 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Research Article |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Haziran 2021 |
| Gönderilme Tarihi | 16 Nisan 2020 |
| Kabul Tarihi | 18 Aralık 2020 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 70 Sayı: 1 |
Kaynak Göster
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
