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@article{1115834, author = {Šimon Hilscher, Roman and Zemánek, Petr}, article_location = {Berlín}, article_number = {232}, doi = {http://dx.doi.org/10.1186/1687-1847-2013-232}, keywords = {Discrete symplectic system; Eigenvalue; Weyl-Titchmarsh theory; M-lambda function; Square summable solution; Jointly varying endpoints; Periodic endpoints}, language = {eng}, issn = {1687-1847}, journal = {Advances in Difference Equations}, title = {Weyl disks and square summable solutions for discrete symplectic systems with jointly varying endpoints}, volume = {2013}, year = {2013} }
TY - JOUR ID - 1115834 AU - Šimon Hilscher, Roman - Zemánek, Petr PY - 2013 TI - Weyl disks and square summable solutions for discrete symplectic systems with jointly varying endpoints JF - Advances in Difference Equations VL - 2013 IS - 232 SP - 1-18 EP - 1-18 PB - Springer SN - 16871847 KW - Discrete symplectic system KW - Eigenvalue KW - Weyl-Titchmarsh theory KW - M-lambda function KW - Square summable solution KW - Jointly varying endpoints KW - Periodic endpoints N2 - 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. ER -
ŠIMON HILSCHER, Roman and Petr ZEMÁNEK. Weyl disks and square summable solutions for discrete symplectic systems with jointly varying endpoints. \textit{Advances in Difference Equations}. Berlín: Springer, vol.~2013, No~232, p.~1-18. ISSN~1687-1847. doi:10.1186/1687-1847-2013-232. 2013.
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