Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F03%3A00008168" target="_blank" >RIV/00216224:14310/03:00008168 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions
Original language description
This paper contains a complete characterization of the nonnegativity of a discrete quadratic functional with one endpoint allowed to vary. In particular, we derive the exact form and explain the role of the (strengthened) Legendre condition in the discrete calculus of variations. Under this condition, the nonnegativity the quadratic functional is equivalent to each of the following conditions: the nonexistence of intervals conjugate to 0, the existence of a certain conjoined basis of the associated Jacobi difference equation, the nonnegativity of certain recurrence matrices, and, under a natural additional assumption, the existence of a symmetric solution to the Riccati matrix difference equation. Moreover, an extension of the discrete Legendre condition is derived for the given discrete variational problem.
Czech name
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Czech description
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Project
<a href="/en/project/GA201%2F01%2F0079" target="_blank" >GA201/01/0079: Qualitative theory of solutions of difference equations</a>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2003
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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