Almost Automorphic Functions

Gaston M. N’Guérékata
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Gaston M. N’Guérékata: Morgan State University, Department of Mathematics

Chapter Chapter 2 in Almost Periodic and Almost Automorphic Functions in Abstract Spaces, 2021, pp 17-35 from Springer

Abstract: Abstract Let 𝕏 $$\mathbb X$$ be a (real or complex) Banach space and f ∈ C ( ℝ , 𝕏 ) $$f\in C(\mathbb R,\mathbb X)$$ . We say that f is almost automorphic if for every sequence of real numbers ( s n ′ ) $$(s^{\prime }_n)$$ there exists a subsequence (s n) such that lim m → ∞ lim n → ∞ f ( t + s m − s n ) = f ( t ) $$\displaystyle \displaystyle \lim _{m\to \infty }\displaystyle \lim _{n\to \infty }f(t+s_m-s_n)=f(t) $$ for each t ∈ ℝ $$t\in \mathbb R$$ .

Date: 2021
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DOI: 10.1007/978-3-030-73718-4_2

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