An asymptotic expansion of the solution of a matrix difference equation of general form

被引：0

作者：

Sgibnev, M. S. ^{[1
]}

机构：

[1] Russian Acad Sci, Sobolev Inst Math, Siberian Div, Novosibirsk, Russia

来源：

SBORNIK MATHEMATICS | 2014年 / 205卷 / 12期

关键词：

matrix difference equation; unbounded delay; characteristic equation; submultiplicative function; asymptotic behaviour; Banach algebra;

D O I：

10.1070/SM2014v205n12ABEH004441

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1815 / 1828

页数：14

共 14 条

[1]

[Anonymous], 1977, APPL MATH SCI

[2]

Feller W., 1966, An introduction to probability theory and its applications, V2

[3]

Hille E., 1957, Amer. Math. Soc. Colloq. Publ., V31

[4]

Horn R.A., 2012, Matrix Analysis

[5]

Lancaster P., 1969, Theory of matrices

[6] Estimates of the solutions of difference-differential equations of neutral type [J].

Lesnykh, A. A. .

MATHEMATICAL NOTES, 2007, 81 (3-4) :503-517

[7]

MARKUSHEVICH A., 1967, THEORY ANAL FUNCTION, V1

[8]

ROGOZIN BA, 1980, SIBERIAN MATH J+, V21, P265

[9] Asymptotics of solutions of an integro-differential and an integral equation [J].

Sgibnev, M. S. .

DIFFERENTIAL EQUATIONS, 2006, 42 (09) :1291-1301

[10] Behavior at infinity of a solution to a matrix differential-difference equation [J].

Sgibnev, M. S. .

SIBERIAN MATHEMATICAL JOURNAL, 2014, 55 (03) :530-543

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