Weyl disks and square summable solutions for discrete symplectic systems with jointly varying endpoints

Advances in Difference Equations

Roman imon Hilscher¹ 

[1] Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic

关键词: discrete symplectic system;    eigenvalue;    Weyl-Titchmarsh theory;    M-lambda function;    square summable solution;    jointly varying endpoints;    periodic endpoints;   

DOI  :  10.1186/1687-1847-2013-232

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper we develop the spectral theory for discrete symplectic systems with general jointly varying endpoints. This theory includes a characterization of the eigenvalues, construction of the M-lambda function and Weyl disks, their matrix radii and centers, statements about the number of square summable solutions, and limit point or limit circle analysis. These results are new even in some particular cases, such as for the periodic and antiperiodic endpoints, or for discrete symplectic systems with special linear dependence on the spectral parameter. The method utilizes a new transformation to separated endpoints, which is simpler and more transparent than the one in the known literature. MSC: 39A12, 34B20, 34B05, 47B39.

【 授权许可】

CC BY