Generalisation of the Frobenius Formula in the Theory of Block Operators on Normed Spaces

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...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 9; no. 23; p. 3066
Main Authors: Sidorov, Nikolai A., Dreglea, Aliona I., Sidorov, Denis N.
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.12.2021
Subjects:
Approximation
asymptotic approximations
Banach spaces
block operators
Existence theorems
Formulas (mathematics)
Fredholm operator
Frobenius formula
Linear equations
Mathematics
Neighborhoods
Nekrasov–Nazarov method
operator theory
Operators (mathematics)
Partial differential equations
Theorems
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math9233066