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@article{1210406, author = {Šepitka, Peter and Šimon Hilscher, Roman}, article_number = {March}, doi = {http://dx.doi.org/10.1016/j.laa.2014.11.029}, keywords = {Recessive solution; Discrete symplectic system; Nonoscillation; Minimal recessive solution; Controllability; Conjoined basis; Order of abnormality; Moore-Penrose pseudoinverse}, language = {eng}, issn = {0024-3795}, journal = {Linear Algebra and Its Applications}, title = {Recessive solutions for nonoscillatory discrete symplectic systems}, volume = {469}, year = {2015} }
TY - JOUR ID - 1210406 AU - Šepitka, Peter - Šimon Hilscher, Roman PY - 2015 TI - Recessive solutions for nonoscillatory discrete symplectic systems JF - Linear Algebra and Its Applications VL - 469 IS - March SP - 243-275 EP - 243-275 PB - Elsevier SN - 00243795 KW - Recessive solution KW - Discrete symplectic system KW - Nonoscillation KW - Minimal recessive solution KW - Controllability KW - Conjoined basis KW - Order of abnormality KW - Moore-Penrose pseudoinverse N2 - In this paper we introduce a new concept of a recessive solution for discrete symplectic systems, which does not require any eventual controllability assumption. We prove that the existence of a recessive solution is equivalent with the nonoscillation of the system and that recessive solutions can have any rank between explicitly given lower and upper bounds. The smallest rank corresponds to the minimal recessive solution, which is unique up to a right nonsingular multiple, while the largest rank yields the traditional maximal recessive solution. We also present a method for constructing some (but not all) recessive solutions having a block diagonal structure from systems in lower dimension. Our results are new even for special discrete symplectic systems, such as for even order Sturm--Liouville difference equations and linear Hamiltonian difference systems. ER -
ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Recessive solutions for nonoscillatory discrete symplectic systems. \textit{Linear Algebra and Its Applications}. Elsevier, 2015, roč.~469, March, s.~243-275. ISSN~0024-3795. Dostupné z: https://dx.doi.org/10.1016/j.laa.2014.11.029.
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