Abstract
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.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 171, Proceedings of the Voronezh Winter Mathematical School “Modern Methods of Function Theory and Related Problems,” Voronezh, January 28 – February 2, 2019. Part 2, 2019.
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Vysotskaya, I.A. Solutions of Difference Equations Almost Periodic at Infinity. J Math Sci 263, 635–642 (2022). https://doi.org/10.1007/s10958-022-05954-1
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DOI: https://doi.org/10.1007/s10958-022-05954-1
Keywords and phrases
- function almost periodic at infinity
- function slowly changing at infinity
- function integrally decreasing at infinity
- difference equation