Pseudo Almost Automorphy

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

Chapter Chapter 5 in Almost Periodic and Almost Automorphic Functions in Abstract Spaces, 2021, pp 55-63 from Springer

Abstract: Abstract Let A A 0 ( 𝕏 ) $$AA_0(\mathbb X)$$ , ϕ ∈ B C ( ℝ , 𝕏 ) $$\phi \in BC(\mathbb R,\mathbb X)$$ such that lim T → ∞ 1 2 T ∫ − T T ∥ ϕ ( t ) ∥ d t = 0 , $$\displaystyle \displaystyle \lim _{T\to \infty }\frac {1}{2T}\int _{-T}^{T}\|\phi (t)\|dt=0, $$ (resp. A A 0 ( ℝ × 𝕏 ) $$AA_0(\mathbb R\times \mathbb X)$$ the set of all functions ϕ ∈ B C ( ℝ × 𝕏 , 𝕏 ) $$\phi \in BC(\mathbb R\times \mathbb X,\mathbb X)$$ such that lim T → ∞ 1 2 T ∫ − T T ∥ ϕ ( t , x ) ∥ d t = 0 $$\displaystyle \displaystyle \lim _{T\to \infty }\frac {1}{2T}\int _{-T}^{T}\|\phi (t,x)\|dt=0 $$ uniformly for x in any bounded set of 𝕏 $$\mathbb X$$ .)

Date: 2021
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DOI: 10.1007/978-3-030-73718-4_5

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