Generalized Vectorial Almost Periodicity
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Authors: M. KOSTIć
DOI: 10.46793/KgJMat2609.1481K
Abstract:
In this paper, we introduce and analyze several new classes of generalized vectorially almost periodic functions. We also analyze Σ-almost periodic type functions and the invariance of generalized vectorial almost periodicity under the actions of convolution products.
Keywords:
Vectorially Stepanov almost periodic function, vectorially Weyl almost periodic function, Σ-almost periodic function, convolution invariance.
References:
[1] S. Abbas and M. Kostić, Metrical Weyl almost automorphy and applications, Adv. Pure Appl. Math. (accepted). https://www.openscience.fr/Metrical-Weyl-almost-automorphy-and-applications
[2] J. Andres, A. M. Bersani and R. F. Grande, Hierarchy of almost-periodic function spaces, Rend. Mat. Appl. 26(7) (2006), 121–188.
[3] J. Andres and D. Pennequin, On the nonexistence of purely Stepanov almost-periodic solutions of ordinary differential equations, Proc. Amer. Math. Soc. 140 (2012), 2825–2834.
[4] W. Arendt, C. J. K. Batty, M. Hieber and F. Neubrander, Vector-valued Laplace Transforms and Cauchy Problems, Monographs in Mathematics, Vol. 96, Birkhäuser, Basel, 2001.
[5] B. Basit and H. Güenzler, Spectral criteria for solutions of evolution equations and comments on reduced spectra, Far East J. Math. Sci. (FJMS) 65 (2012), 273–288.
[6] A. S. Besicovitch, Almost Periodic Functions, Dover Publ., New York, 1954.
[7] S. Bochner, Curvature and Betti numbers in real and complex vector bundles, Rend. Semin. Mat. Univ. Politec. Torino 15 (1955–1956).
[8] C. Budde and J. Kreulich, On splittings and integration of almost periodic functions with and without geometry, Semigroup Forum 108 (2024), 335–364.
[9] T. Diagana, Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, Springer-Verlag, New York, 2013.
[10] H.-S. Ding, W-G. Jian, N. V. Minh and G. M. N’Guérékata, Kadets type and Loomis type theorems for asymptotically almost periodic functions, J. Diff. Equ. 373 (2023), 389–410.
[11] A. M. Fink, Almost Periodic Differential Equations, Springer-Verlag, Berlin, 1974.
[12] G. M. N’Guérékata, Almost Automorphic and Almost Periodic Functions in Abstract Spaces, Kluwer Acad. Publ, Dordrecht, 2001.
[13] M. Kostić, Abstract Volterra Integro-Differential Equations, CRC Press, Boca Raton, Fl., 2015.
[14] M. Kostić, Almost Periodic and Almost Automorphic Type Solutions to Integro-Differential Equations, W. de Gruyter, Berlin, 2019.
[15] M. Kostić, Selected Topics in Almost Periodicity, W. de Gruyter, Berlin, 2022.
[16] M. Kostić, Metrical Almost Periodicity and Applications to Integro-Differential Equations, W. de Gruyter, Berlin, 2023.
[17] M. Kostić, Metrical almost periodicity and applications, Ann. Polon. Math. 129 (2022), 219–254.
[18] M. Kostić and W.-S. Du, Stepanov almost periodic type functions and applications to abstract impulsive Volterra integro-differential inclusions, Fractal Fract. (2023), Article ID 736. https://doi.org/10.3390/fractalfract7100736
[19] M. Kostić, V. E. Fedorov and H. C. Koyuncuoğlu, Metrical Bochner criterion and metrical Stepanov almost periodicity, Chelj. Phy. Math. J. 9 (2024), 90–100.
[20] M. Levitan, Almost Periodic Functions, G.I.T.T.L., Moscow, 1953 (in Russian).
[21] A. M. Samoilenko and S. I. Trofimchuk, Unbounded functions with almost periodic differences, Ukrainian Math. J. 43 (1992), 1306–1309.
[22] W. Stepanoff, Über einige Verallgemeinerungen der fast periodischen Funktionen, Math. Ann. 95 (1926), 473–498.
[23] S. Zaidman, Almost-Periodic Functions in Abstract Spaces, Pitman Research Notes in Math, Vol. 126, Pitman, Boston, 1985.
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