Araştırma Makalesi
Yıl 2019,
Cilt: 68 Sayı: 2, 1316 - 1334, 01.08.2019
Öz
Kaynakça
- Naimark, M.A., Investigation of the spectrum and the expansion in eigenfunctions of a non-selfadjoint operator of the second order on a semi-axis, American Mathematical Society Translations Series 2, 16, (1960), 103--193.
- Lyance, V.E., A differential operator with spectral singularities I, II, American Mathematical Society Transactions Series 2, 60, (1967), 185--225, 227--283.
- Gasymov, M.G. and Maksudov, F.G., The principal part of the resolvent of non-selfadjoint opeerators in neighbourhood of spectral singularities, Func. Anal. Appl, 6, (1972), 185--192.
- Maksudov, F.G. and Allakhverdiev, B.P., Spectral analysis of a new class of non-selfadjoint operators with continuous and point spectrum, Soviet Math. Dokl., 30, (1984), 566--569.
- Adıvar, M. and Bairamov, E., Spectral properties of non-selfadjoint difference operators, Journal of Mathematical Analysis and Applications, 261(2), (2001), 461--478.
- Bairamov, E., Çakar, Ö. and Yanık, C., Spectral singularities of the Klein-Gordon s-wave equation, Indian Journal of Pure and Applied Mathematics, 32(6), (2001), 851--857.
- Bairamov, E. and Çelebi, A.O., Spectrum and spectral expansion for the non-selfadjoint discrete Dirac operators, The Quarterly Journal of Mathematics. Oxford Second Series, 50(200), (1999), 371--384.
- Bairamov, E. and Karaman, Ö., Spectral singularities of the Klein-Gordon s-wave equations with and integral boundary conditions, Acta Mathematica Hungarica, 97(1--2), (2002), 121--131.
- Krall, A.M., Bairamov, E. and Çakar, Ö., Spectrum and spectral singularities of a quadratic pencil of a Schrödinger operator with a general boundary condition, Journal of Differential Equations, 151(2), (1999), 252--267.
- Krall, A.M., Bairamov, E. and Çakar, Ö., Spectral analysis of non-selfadjoint discrete Schrödinger operators with spectral singularities, Mathematische Nachrichten, 231, (2001), 89--104.
- Marchenko, V.A., Expansion in eigenfunctions of non-selfadjoint singular second-order differential operators, American Mathematical Society Transactions Series 2, 25, (1963), 99.77--130.
- Başcanbaz-Tunca, G, Spectral expasion of a non-selfadjoint differential operator on the whole axis, J.Math.Anal.Appl., 252(1), (2000), 278--297.
- Kır Arpat, E., An eingenfunction expansion of the non-selfadjoint Sturm-Liouville operator with a singular potential, Journal of Mathematical Chemistry, 51(8), (2013), 2196--2213.
- Bairamov, E. and Yokuş, N., Spectral singularities of Sturm-Liouville problems with eigenvalue-dependent boundary conditions, Abstract and Applied Analysis, 2009, Article ID 289596, (2009), 8 pages.
- Yokuş, N., Principal functions of non-selfadjoint sturm-liouville problems with eigenvalue-dependent boundary conditions, Abstract and Applied Analysis, 2011, Article ID 358912, (2011), 12 pages.
Yıl 2019,
Cilt: 68 Sayı: 2, 1316 - 1334, 01.08.2019
Öz
In this paper, we consider the operator L generated in L₂(R₊) by the differential expression
l(y)=-y′′+q(x)y,x∈R₊:=[0,∞)
and the boundary condition
((y′(0))/(y(0)))=α₀+α₁λ+α₂λ²,
where q is a complex valued function and α_{i}∈C,[mbox]<LaTeX>\mbox{\:}</LaTeX>i=0,1,2α₂. We have proved that spectral expansion of L in terms of the principal functions under the condition
q∈AC(R₊), lim_{x→∞}q(x)=0, sup[e^{ε√x}|q′(x)|]<∞, ε>0
taking into account the spectral singularities. We have also proved the convergence of the spectral expansion.
Anahtar Kelimeler
Eigenvalues spectral singularities principal functions resolvent spectral expansion.
Kaynakça
- Naimark, M.A., Investigation of the spectrum and the expansion in eigenfunctions of a non-selfadjoint operator of the second order on a semi-axis, American Mathematical Society Translations Series 2, 16, (1960), 103--193.
- Lyance, V.E., A differential operator with spectral singularities I, II, American Mathematical Society Transactions Series 2, 60, (1967), 185--225, 227--283.
- Gasymov, M.G. and Maksudov, F.G., The principal part of the resolvent of non-selfadjoint opeerators in neighbourhood of spectral singularities, Func. Anal. Appl, 6, (1972), 185--192.
- Maksudov, F.G. and Allakhverdiev, B.P., Spectral analysis of a new class of non-selfadjoint operators with continuous and point spectrum, Soviet Math. Dokl., 30, (1984), 566--569.
- Adıvar, M. and Bairamov, E., Spectral properties of non-selfadjoint difference operators, Journal of Mathematical Analysis and Applications, 261(2), (2001), 461--478.
- Bairamov, E., Çakar, Ö. and Yanık, C., Spectral singularities of the Klein-Gordon s-wave equation, Indian Journal of Pure and Applied Mathematics, 32(6), (2001), 851--857.
- Bairamov, E. and Çelebi, A.O., Spectrum and spectral expansion for the non-selfadjoint discrete Dirac operators, The Quarterly Journal of Mathematics. Oxford Second Series, 50(200), (1999), 371--384.
- Bairamov, E. and Karaman, Ö., Spectral singularities of the Klein-Gordon s-wave equations with and integral boundary conditions, Acta Mathematica Hungarica, 97(1--2), (2002), 121--131.
- Krall, A.M., Bairamov, E. and Çakar, Ö., Spectrum and spectral singularities of a quadratic pencil of a Schrödinger operator with a general boundary condition, Journal of Differential Equations, 151(2), (1999), 252--267.
- Krall, A.M., Bairamov, E. and Çakar, Ö., Spectral analysis of non-selfadjoint discrete Schrödinger operators with spectral singularities, Mathematische Nachrichten, 231, (2001), 89--104.
- Marchenko, V.A., Expansion in eigenfunctions of non-selfadjoint singular second-order differential operators, American Mathematical Society Transactions Series 2, 25, (1963), 99.77--130.
- Başcanbaz-Tunca, G, Spectral expasion of a non-selfadjoint differential operator on the whole axis, J.Math.Anal.Appl., 252(1), (2000), 278--297.
- Kır Arpat, E., An eingenfunction expansion of the non-selfadjoint Sturm-Liouville operator with a singular potential, Journal of Mathematical Chemistry, 51(8), (2013), 2196--2213.
- Bairamov, E. and Yokuş, N., Spectral singularities of Sturm-Liouville problems with eigenvalue-dependent boundary conditions, Abstract and Applied Analysis, 2009, Article ID 289596, (2009), 8 pages.
- Yokuş, N., Principal functions of non-selfadjoint sturm-liouville problems with eigenvalue-dependent boundary conditions, Abstract and Applied Analysis, 2011, Article ID 358912, (2011), 12 pages.
Toplam 15 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Ağustos 2019 |
| Gönderilme Tarihi | 14 Kasım 2017 |
| Kabul Tarihi | 6 Ağustos 2018 |
| Yayımlandığı Sayı | Yıl 2019 Cilt: 68 Sayı: 2 |
Kaynak Göster
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
