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Inequalities and asymptotics for Riccati matrix difference operators. (English) Zbl 0914.39012
Inequalities for the solutions of the Riccati matrix difference equation $Q_{k+1}= C_k+(I-A_k^T) Q_k(I+B_kQ_k)^{-1} (I-A_k)$ which correspond to the linear Hamiltonian difference system are developed. Finally the asymptotic behaviour of solutions $$Q_k(\lambda)$$, as $$|\lambda|\to \infty$$, of the special Riccati matrix difference equation is established which corresponds to the Sturm-Liouville equation $\sum_{\mu=0}^n (-1)^\mu r_\mu \Delta^{2\mu} y_{k+1-\mu}= \lambda y_{k+1}$ of even order $$2n$$ with constant coefficients $$r_0,\dots, r_n$$.

##### MSC:
 39A12 Discrete version of topics in analysis 39A10 Additive difference equations 39A70 Difference operators
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##### References:
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