An inequality for finite differences via asymptotics of Riccati matrix difference equations
Werner Kratz · The Journal of Difference Equations and Applications · 1998
The paper deals with the Riccati matrix difference equation, which corresponds to the Sturm-Liouville equation of even order namely: with real parameter λ The main thorem states in essence the asymptotic expansion of the principal solution of Riccati's equation as λ→−∞ in terms of negative powers of λVia a discrete Picone type identity the asymptotic result is used to derive an inequality for a discrete quadratic functional containing n thorder differences.