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- Title
Generalisation of the Frobenius Formula in the Theory of Block Operators on Normed Spaces.
- Authors
Sidorov, Nikolai A.; Dreglea, Aliona I.; Sidorov, Denis N.
- Abstract
The efficient construction and employment of block operators are vital for contemporary computing, playing an essential role in various applications. In this paper, we prove a generalisation of the Frobenius formula in the setting of the theory of block operators on normed spaces. A system of linear equations with the block operator acting in Banach spaces is considered. Existence theorems are proved, and asymptotic approximations of solutions in regular and irregular cases are constructed. In the latter case, the solution is constructed in the form of a Laurent series. The theoretical approach is illustrated with an example, the construction of solutions for a block equation leading to a method of solving some linear integrodifferential system.
- Subjects
OPERATOR theory; OPERATOR equations; GENERALIZATION; EXISTENCE theorems; FREDHOLM operators; LAURENT series; NORMED rings
- Publication
Mathematics (2227-7390), 2021, Vol 9, Issue 23, p3066
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math9233066