Spectral properties of non-selfadjoint Sturm–Liouville operator with operator coefficient

Spectral properties of non-selfadjoint Sturm-Liouville operator equation on the real axis

“…The proofs of above results are very similar to the matrix coefficient case which have been obtained in [1,4]. In addition, we obtained analogous properties in our previous paper [3]. Hence, we omitted the proofs.…”

“…Equation (1.4) is called Sturm-Liouville operator equation. In our previous paper [3], we considered the non-selfadjoint analogue of the above problem and investigated the spectral properties of the non-selfadjoint Sturm-Liouville operator equation on the half line on the contrary to [14,[19][20][21]. We also generalized the results in [2,4,11,26,27] by considering the coefficients as operators not only finite dimensional matrices.…”

Spectrum of Discrete Sturm-Liouville Equation with Self-adjoint Operator Coefficients on the Half-line

“…Recently, spectral properties of the non-self-adjoint operator which is generated by expression (4) with non-self-adjoint operator coefficients in an infinite dimensional Hilbert space and Dirichlet boundary condition has been studied (Bairamov et al, 2017). The discrete spectrum and the spectral singularities were obtained and the finiteness of eigenvalues and spectral singularities was proven (Bairamov et al, 2017). Further, these results have been extended to whole real line (Mutlu and Kir Arpat 2020a).…”

“…The discrete spectrum of the operator generated by 𝑙 0 and the boundary condition 𝑦 0 = 0 has been studied (Gasymov et al, 1967). Recently, spectral properties of the non-self-adjoint operator which is generated by expression (4) with non-self-adjoint operator coefficients in an infinite dimensional Hilbert space and Dirichlet boundary condition has been studied (Bairamov et al, 2017). The discrete spectrum and the spectral singularities were obtained and the finiteness of eigenvalues and spectral singularities was proven (Bairamov et al, 2017).…”

“…Studies on Sturm-Liouville differential and difference equations with matrix or operator coefficients have grown extensively in recent years (Bairamov et al, 2017;Mutlu, 2020;Mutlu and Kir Arpat 2020a;Mutlu and Kir Arpat 2020b;Aktosun and Weder, 2020). In particular, spectral properties of Sturm-Liouville differential (Aktosun and Weder, 2020) and difference equations (Aygar and Bairamov, 2012;Bairamov et al, 2016) with hermitian matrix coefficients have been examined.…”