Geodesic
Almost periodic at infinity solutions of difference equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 38-46

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We consider a new class of functions almost periodic at infinity defined by using the subspace of functions that integrally decrease at infinity. We propose four definitions of functions almost periodic at infinity and prove their equivalence. Also, we obtain spectral criteria of almost periodicity at infinity of bounded solutions of systems of linear difference equations and their asymptotic representation.
Keywords: function almost periodic at infinity, function slowly changing at infinity, function integrally decreasing at infinity, difference equation. 
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     author = {I. A. Vysotskaya},
     title = {Almost periodic at infinity solutions of difference equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {38--46},
     publisher = {mathdoc},
     volume = {171},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_171_a2/}
}
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I. A. Vysotskaya. Almost periodic at infinity solutions of difference equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 38-46. http://geodesic.mathdoc.fr/item/INTO_2019_171_a2/