Bouzar, Chikh; Tchouar, Fatima Zahra Asymptotic almost automorphy of functions and distributions. (English) Zbl 1448.42016 Ural Math. J. 6, No. 1, 54-70 (2020). Summary: This work aims to introduce and to study asymptotic almost automorphy in the context of Sobolev-Schwartz distributions. Applications to linear ordinary differential equation and neutral difference differential equations are also given. Cited in 1 Document MSC: 42A75 Classical almost periodic functions, mean periodic functions 34C25 Periodic solutions to ordinary differential equations Keywords:asymptotically almost automorphic functions; asymptotically almost automorphic distributions; neutral difference differential equations PDF BibTeX XML Cite \textit{C. Bouzar} and \textit{F. Z. Tchouar}, Ural Math. J. 6, No. 1, 54--70 (2020; Zbl 1448.42016) Full Text: DOI MNR OpenURL References: [1] Bochner S., “Uniform convergence of monotone sequences of functions”, Proc. Natl. Acad. Sci. USA, 47:4 (1961), 582-585 · Zbl 0103.05304 [2] Bochner S., “A new approach to almost periodicity”, Proc. Natl. Acad. Sci. USA, 48:12 (1962) · Zbl 0112.31401 [3] Bochner S., “Continuous mappings of almost automorphic and almost periodic functions”, Proc. Natl. Acad. Sci. USA, 52:4 (1964), 907-910 · Zbl 0134.30102 [4] Bohr H., Almost Periodic Functions, Chelsea Publishing Company, 1947, 113 pp. · Zbl 0005.20303 [5] Bouzar C., Khalladi M. T., Tchouar F.Ż., “Almost automorphic generalized functions”, Novi Sad J. Math., 45:1 (2015), 207-214 · Zbl 1450.43004 [6] Bouzar C., Tchouar F.Ż., “Almost automorphic distributions”, Mediterr. J. Math., 2017, no. 151 · Zbl 1390.46041 [7] Cioranescu I., “Asymptotically almost periodic distributions”, Appl. Anal, 34:3-4. (1990), 251- 259 · Zbl 0661.46031 [8] Levitan B. M., Zhikov V. V., Almost Periodic Functions and Differential Equations, Cambridge University Pres, 1982, 224 pp. · Zbl 0499.43005 [9] Fréchet M., “Les fonctions asymptotiquement presque périodiques”, Revue Sci., 79 (1941), 341-354 · JFM 67.1010.03 [10] Kostić M., Asymptotically Almost Periodic and Asymptotically Almost Automorphic Vector Valued Generalized Functions, 2018, 18 pp., arXiv: · Zbl 1424.45021 [11] Kostić M., Pilipovi ć S., Velinov D., “Quasi-asymptotically almost periodic vector-valued generalized functions”, Sarajevo J. Math., 15:28 (2019), 181-199 · Zbl 1449.46030 [12] N“Guérékata G. M., “Some remarks on asymptotically almost automorphic functions”, Riv. Math. Univ. Parma, 13 (1987), 301-303 [13] Schwartz L., Théorie des Distributions, Hermann, DL, Paris, 1966 · Zbl 0149.09501 [14] Seeley R. T, “Extension of C1 functions defined in a half space”, Proc. Amer. Math. Soc., 15:4 (1964), 625-626 · Zbl 0127.28403 [15] Sobolev S. L., Applications of Functional Analysis in Mathematical Physics, American Mathematical Society, 1963, 239 pp. · Zbl 0123.09003 [16] Stepanov V. V., “Sur Quelques Généralisations des Fonctions Presque Périodiques”, C.R. Acad. Sci. Paris, 181 (1925), 90-92 · JFM 51.0214.01 [17] Tchouar F.Ż., Asymptotically almost automorphic generalized functions, Abstr. of the Int. Conf. GF 2016 (September 4-9, 2016), Dubrovnik, 67 [18] Zaki M., “Almost automorphic solutions of certain abstract differential equations”, Ann. Mat. Pura Appl., 4 (1974), 91-114 · Zbl 0304.42028 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.