Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems

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Publikace nespadá pod Fakultu sportovních studií, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
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DOŠLÝ Ondřej HILSCHER Roman ZEIDAN Vera

Rok publikování 2003
Druh Článek v odborném periodiku
Časopis / Zdroj Linear Algebra and its Applications
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
Obor Obecná matematika
Klíčová slova Symplectic difference system; Discrete quadratic functional; Nonnegativity; Positivity; Focal point; Conjoined basis; Riccati difference equation; Linear Hamiltonian difference system
Popis We study the nonnegativity of quadratic functionals with separable endpoints which are related to the discrete symplectic system (S). In particular, we characterize the nonnegativity of these functionals in terms of (i) the focal points of the natural conjoined basis of (S) and (ii) the solvability of an implicit Riccati equation associated with (S). This result is closely related to the kernel condition for the natural conjoined basis of (S). We treat the situation when this kernel condition is possibly violated at a certain index. To accomplish this goal, we derive a new characterization of the set of admissible pairs (sequences) that does not require the validity of the above mentioned kernel condition. Finally, we generalize our results to the variable stepsize case.
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