Dirichlet-to-Robin maps on finite networks

Applicable Analysis and Discrete Mathematics

article

Cristina Araúz¹  Ángeles Carmona¹  Andrés M. Encinas¹ 

[1] Matem`atica Aplicada III, Universitat Polit`ecnica de Catalunya Spain

关键词: Finite networks;    Schrödinger operator;    Dirichlet-to-Robin map;    Schur complement;    Inverse problem;   

DOI  :  10.2298/AADM150207004A

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

Our aim is to characterize those matrices that are the response matrix ofa semi–positive definite Schr¨odinger operator on a circular planar network.Our findings generalize the known results and allow us to consider both nonsingular and non diagonally dominant matrices as response matrices. To thisend, we define the Dirichlet–to–Robin map associated with a Schr¨odingeroperator on general networks, and we prove that it satisfies the alternatingproperty which is essential to characterize the response matrices.

【 授权许可】

Unknown