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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Vydáno v:Mathematics (Basel) Ročník 9; číslo 23; s. 3066
Hlavní autoři: Sidorov, Nikolai A., Dreglea, Aliona I., Sidorov, Denis N.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.12.2021
Témata:
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
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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.
AbstractList 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.
Author Sidorov, Denis N.
Sidorov, Nikolai A.
Dreglea, Aliona I.
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  givenname: Denis N.
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  surname: Sidorov
  fullname: Sidorov, Denis N.
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Cites_doi 10.1134/S1995080219050068
10.14529/mmp170205
10.1007/978-94-017-2122-6
10.1007/978-94-009-0369-2_9
10.1134/S0012266109120155
10.1515/9783110378443
10.1007/s11253-019-01662-3
10.1007/978-3-319-17566-9
10.1070/SM1995v186n02ABEH000017
10.1007/978-3-642-53393-8
10.5948/9781614442134
10.3182/20080706-5-KR-1001.01676
10.1142/p493
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Copyright 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
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References ref_14
Lusternik (ref_17) 1956; 72
Sidorov (ref_20) 2010; 45
ref_10
ref_19
ref_18
Akhmedov (ref_24) 1957; 12
Balandin (ref_13) 2008; 41
Monaco (ref_12) 2002; 42
Gokhberg (ref_23) 1957; 12
Zhuravlev (ref_11) 2019; 71
Sidorov (ref_16) 1995; 186
ref_25
ref_22
ref_21
ref_1
ref_3
Boglaev (ref_2) 1979; 20
ref_9
ref_8
Erofeev (ref_15) 2019; 40
ref_5
ref_4
ref_7
ref_6
References_xml – volume: 72
  start-page: 145
  year: 1956
  ident: ref_17
  article-title: Some questions of nonlinear functional analysis
  publication-title: Uspehi Mat. Nauk
– ident: ref_3
– volume: 42
  start-page: 1403
  year: 2002
  ident: ref_12
  article-title: The Frobenius formula and Sherman–Morrison formulas and related matters
  publication-title: Comput. Math. Math. Phys.
– volume: 40
  start-page: 547
  year: 2019
  ident: ref_15
  article-title: High-performance processing of covariance matrices using GPU computations
  publication-title: Lobachevskii J. Math.
  doi: 10.1134/S1995080219050068
– ident: ref_19
  doi: 10.14529/mmp170205
– ident: ref_9
  doi: 10.1007/978-94-017-2122-6
– volume: 12
  start-page: 135
  year: 1957
  ident: ref_24
  article-title: The analytic method of Nekrasov–Nazarov in non-linear analysis
  publication-title: Uspekhi Mat. Nauk
– ident: ref_1
– ident: ref_18
– ident: ref_14
  doi: 10.1007/978-94-009-0369-2_9
– ident: ref_21
– volume: 45
  start-page: 1840
  year: 2010
  ident: ref_20
  article-title: Nonlinear operator equations with a functional perturbation of the argument of neutral type
  publication-title: Differ. Eqs.
  doi: 10.1134/S0012266109120155
– ident: ref_5
  doi: 10.1515/9783110378443
– ident: ref_8
– ident: ref_25
– ident: ref_10
– volume: 71
  start-page: 471
  year: 2019
  ident: ref_11
  article-title: Conditions of solvability and representation of the solutions of equations with operator matrices
  publication-title: Ukr. Math. J.
  doi: 10.1007/s11253-019-01662-3
– ident: ref_6
  doi: 10.1007/978-3-319-17566-9
– volume: 12
  start-page: 43
  year: 1957
  ident: ref_23
  article-title: Fundamental aspects of defect numbers, root numbers and indexes of linear operators
  publication-title: Uspekhi Mat. Nauk
– volume: 186
  start-page: 297
  year: 1995
  ident: ref_16
  article-title: Explicit and implicit parametrizations in the construction of branching solutions by iterative methods
  publication-title: Sb. Math.
  doi: 10.1070/SM1995v186n02ABEH000017
– ident: ref_4
  doi: 10.1007/978-3-642-53393-8
– ident: ref_22
  doi: 10.5948/9781614442134
– volume: 20
  start-page: 731
  year: 1979
  ident: ref_2
  article-title: The generalized Frobenius formula in singularly perturbed linear equations
  publication-title: Sov. Math. Dokl.
– volume: 41
  start-page: 9905
  year: 2008
  ident: ref_13
  article-title: LMI based output-feedback controllers: γ-optimal versus linear quadratic
  publication-title: IFAC Proc. Vol.
  doi: 10.3182/20080706-5-KR-1001.01676
– ident: ref_7
  doi: 10.1142/p493
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SubjectTerms 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
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