@article{Du2023, 
author = {Gaofeng Du and Chenghua Gao and Jingjing Wang},
title = {Spectral analysis of discontinuous Sturm-Liouville operators with Herglotzs transmission},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {4},
pages = {2108-2119},
keywords = {spectral analysis, Sturm-Liouville operator, transmission conditions, eigenparameter dependent boundary condition, eigenvalue problem},
url = {https://www.sciopen.com/article/10.3934/era.2023108},
doi = {10.3934/era.2023108},
abstract = {In this paper, we study the spectral properties of the Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions. In details, we introduce a Hilbert space formula, so that the problem we consider can be interpreted as an eigenvalue problem of an self-adjoint operator. Moreover, the Green's function and the resolvent of the related linear operator are obtained.}
}