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

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.

UDC: 517.929.8

PACS: 02.30.Ks

MSC: 39A06, 39A22

Received: 27.12.2013 and 18.08.2014

DOI: 10.4213/sm8319

 English version: Sbornik: Mathematics, 2014, 205:12, 1815–1828

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