Publication details
Picone type identities and definiteness of quadratic functionals on time scales
| Authors | |
|---|---|
| Year of publication | 2009 |
| Type | Peer-reviewed scientific article |
| Magazine / Source | Applied Mathematics and Computation |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | Time scale; Time scale symplectic system; Linear Hamiltonian system; Discrete symplectic system; Picone identity; Quadratic functional; Nonnegativity; Positivity; Conjoined basis; Controllability; Normality |
| Description | In this paper we derive a new sufficient condition for the nonnegativity of time scale quadratic functionals associated to time scale symplectic systems. To establish this result, a new global Picone formula is derived. Another proof of a special case of the result is shown to be obtained via a Sturmian comparison technique. Furthermore, we derive several new Picone type identities which, in particular, do not impose a certain delta-differentiability assumption, and we survey known ones from the literature. The results in this paper complete our earlier work on the definiteness of a time scale quadratic functional in terms of its corresponding time scale symplectic system. |
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