Generalisation of the frobenius formula in the theory of block operators on normed spaces
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.
Библиографическая ссылка
Sidorov D.N., Sidorov N.A., Dreglea A.I. Generalisation of the frobenius formula in the theory of block operators on normed spaces // Mathematics. Vol.23. No.9. 2021. DOI: 10.3390/math9233066WOS
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