The determinants of dissipative Sturm–Liouville operators with transmission conditions

Abstract

a b s t r a c tIn this paper, we study the determinant of perturbation connected with the dissipative operator L generated in L 2 (I) by (1.1)-(1.5). Then using Livšic's theorem, we investigate the problem of completeness of the system of eigenfunctions and associated functions of L.

Dissipative Sturm-Liouville Operators with Transmission Conditions

“…All the maximal dissipative extensions L of the operator 0 are described by the following conditions (see [4,15,18]):…”

“…There has recently been great interest in spectral analysis of Sturm-Liouville boundary value problems with eigenparameter-dependent boundary conditions (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14]). Furthermore, many researchers have studied some boundary value problems that may have discontinuities in the solution or its derivative at an interior point [15][16][17][18][19]. Such conditions which include left and right limits of solutions and their derivatives at are often called "transmission conditions" or "interface conditions. "…”

The one‐dimensional Schrödinger operator on bounded time scales

“…Finally, we prove a theorem on completeness of the system of eigenvectors and associated vectors of dissipative operators under consideration. A similar way was employed earlier in the case of differential and difference operators in [12][13][14][15][16][17][18].…”

Bir Boyutlu Dirac Operatörlerinin Özfonksiyonlar Sisteminin Tamlığı

“…We prove the theorems on completeness of the system of eigenvectors and associated vectors of the dissipative Dirac operator using Krein's theorems. A similar way was employed earlier in [3], [4], [11], [12], [30]- [33]. †…”