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Sbornik: Mathematics, 2014, Volume 205, Issue 12, Pages 1815–1828
DOI: https://doi.org/10.1070/SM2014v205n12ABEH004441 (Mi sm8319) 		 
An asymptotic expansion of the solution of a matrix difference equation of general form

M. S. Sgibnev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
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DOI: https://doi.org/10.1070/SM2014v205n12ABEH004441
Abstract: An asymptotic expansion of the solution of an inhomogeneous matrix difference equation of general form is obtained. The case when there is no bound on the differences of the arguments is considered. The effect of the roots of the characteristic equation is taken into account. An integral estimate with a submultiplicative weight is established for the remainder in terms of the submultiplicative moment of the free term of the equation.
Bibliography: 14 titles.
Keywords: matrix difference equation, unbounded delay, characteristic equation, submultiplicative function, asymptotic behaviour, Banach algebra.
Received: 27.12.2013 and 18.08.2014
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 12, Pages 141–154
DOI: https://doi.org/10.4213/sm8319
Bibliographic databases:
Document Type: Book
UDC: 517.929.8
PACS: 02.30.Ks
MSC: 39A06, 39A22
Language: English
Original paper language: Russian
Citation: M. S. Sgibnev, “An asymptotic expansion of the solution of a matrix difference equation of general form”, Mat. Sb., 205:12 (2014), 141–154; Sb. Math., 205:12 (2014), 1815–1828
Citation in format AMSBIB
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    Abstract page:414
    Russian version PDF:145
    English version PDF:9
    References:71
    First page:33
     
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