CLARK, Stephen L. and Petr ZEMÁNEK. On discrete symplectic systems: associated maximal and minimal linear relations and nonhomogeneous problems. Journal of Mathematical Analysis and Applications. Elsevier, 2015, vol. 421, No 1, p. 779-805. ISSN 0022-247X. Available from: https://dx.doi.org/10.1016/j.jmaa.2014.07.015. |
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@article{1188470, author = {Clark, Stephen L. and Zemánek, Petr}, article_number = {1}, doi = {http://dx.doi.org/10.1016/j.jmaa.2014.07.015}, keywords = {discrete symplectic system; time-reversed system; definiteness condition; nonhomogeneous problem; Hilbert space; maximal linear relation; minimal linear relation; deficiency index.}, language = {eng}, issn = {0022-247X}, journal = {Journal of Mathematical Analysis and Applications}, title = {On discrete symplectic systems: associated maximal and minimal linear relations and nonhomogeneous problems}, volume = {421}, year = {2015} }
TY - JOUR ID - 1188470 AU - Clark, Stephen L. - Zemánek, Petr PY - 2015 TI - On discrete symplectic systems: associated maximal and minimal linear relations and nonhomogeneous problems JF - Journal of Mathematical Analysis and Applications VL - 421 IS - 1 SP - 779-805 EP - 779-805 PB - Elsevier SN - 0022247X KW - discrete symplectic system KW - time-reversed system KW - definiteness condition KW - nonhomogeneous problem KW - Hilbert space KW - maximal linear relation KW - minimal linear relation KW - deficiency index. N2 - In this paper we characterize the definiteness of the discrete symplectic system, study a nonhomogeneous discrete symplectic system, and introduce the minimal and maximal linear relations associated with these systems. Fundamental properties of the corresponding deficiency indices, including a relationship between the number of square summable solutions and the dimension of the defect subspace, are also derived. Moreover, a sufficient condition for the existence of a densely defined operator associated with the symplectic system is provided. ER -
CLARK, Stephen L. and Petr ZEMÁNEK. On discrete symplectic systems: associated maximal and minimal linear relations and nonhomogeneous problems. \textit{Journal of Mathematical Analysis and Applications}. Elsevier, 2015, vol.~421, No~1, p.~779-805. ISSN~0022-247X. Available from: https://dx.doi.org/10.1016/j.jmaa.2014.07.015.
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