Inequalities and Asymptotics for Riccati Matrix Difference Operators
Abstract
In the first part inequalities for solutions of Riccati matrix difference equations are obtained which correspond to the linear Hamiltonian difference system[formula]whereAk, Bk, Ck, Xk, Ukaren × n-matrices with symmetricBkandCk. If the matricesXkare invertible, then the matricesQk = UkX−1ksolve the Riccati matrix difference equation[formula]In contrast to some recent papers dealing with these equations we do not assume that the matricesBkare invertible. The second part of the paper deals with the asymptotic behaviour of solutionsQk(λ), as|λ| → ∞, of the special Riccati matrix difference equation which corresponds to the Sturm–Liouville equation[formula]of even order 2nwith constant coefficientsr0,…,rn.
Recommended Citation
M. Bohner et al., "Inequalities and Asymptotics for Riccati Matrix Difference Operators," Journal of Mathematical Analysis and Applications, Elsevier, Jan 1998.
The definitive version is available at https://doi.org/10.1006/jmaa.1997.5890
Department(s)
Mathematics and Statistics
International Standard Serial Number (ISSN)
0022-247X
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 1998 Elsevier, All rights reserved.
Publication Date
01 Jan 1998
