Email this article Boundary-Value Problems for the Lyapunov Equation in Banach Spaces
- Authors: Panasenko E.V.1, Pokutnyi O.O.2,3
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Affiliations:
- Zaporizhzhya National University
- Institute of Mathematics, Ukrainian National Academy of Sciences
- Shevchenko Kyiv National University Ukraine
- Issue: Vol 223, No 3 (2017)
- Pages: 298-304
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/239355
- DOI: https://doi.org/10.1007/s10958-017-3356-x
- ID: 239355
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Abstract
We propose an approach to the construction of solutions and quasisolutions of a boundary-value problem for the Lyapunov equation in a Banach space. If the necessary and sufficient conditions for the solvability of this boundary-value problem are satisfied, then the corresponding solutions of the problem are constructed by using the generalized inverse operator. As an example, we consider the problem in the space of bounded sequences with countably dimensional matrices.
About the authors
E. V. Panasenko
Zaporizhzhya National University
Author for correspondence.
Email: panasenko.yevgeniy@gmail.com
Ukraine, Zhukovs’kyi Str., 66, Zaporizhzhya, 69600
O. O. Pokutnyi
Institute of Mathematics, Ukrainian National Academy of Sciences; Shevchenko Kyiv National University Ukraine
Email: panasenko.yevgeniy@gmail.com
Ukraine, Tereshchenkivs’ka Str., 3, Kyiv, 01004; Acad. Glushkov Av. 4e, Kyiv, 03127
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