Geodesic
Stability of a~linear difference equation and estimation of its fundamental solution
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2011), pp. 30-41

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We consider a linear nonautonomous system of difference equations. Under natural restrictions we prove that the stability with respect to the initial function and that with respect to the right-hand side in spaces of bounded and summable functions are equivalent to the corresponding estimates for the fundamential solution. As a consequence, we obtain an effective stability condition for a system with a constant matrix.
Keywords: difference equations, stability, fundamental solution
Mots-clés : effective conditions. 
@article{IVM_2011_12_a3,
     author = {A. Yu. Kulikov and V. V. Malygina},
     title = {Stability of a~linear difference equation and estimation of its fundamental solution},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {30--41},
     publisher = {mathdoc},
     number = {12},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_12_a3/}
}
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A. Yu. Kulikov; V. V. Malygina. Stability of a~linear difference equation and estimation of its fundamental solution. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2011), pp. 30-41. http://geodesic.mathdoc.fr/item/IVM_2011_12_a3/