Sentence examples for be an almost automorphic from inspiring English sources

Let be an almost automorphic function.

Let be an almost automorphic function in for each and assume that satisfies a Lipschitz condition in uniformly in.

(i) [11] Let ({f_{n}}subsetmathbb{R}) be an almost automorphic sequence, and (epsilonin 0,frac{1}{2})). Let (f(t)=f_{n}) if (tin n-epsilon,n+epsilon)) and (f(tin n-epsilonse.

If is an almost automorphic function and is given by (2.5), then.

If is an almost automorphic function and is given by (3.1).

Hence, { φ ( t k ) } is an almost automorphic sequence in X.

Assume that is an almost automorphic function in for each and assume that satisfies a Lipschitz condition in uniformly in.

It is clear that, if (x: mathbb{R}rightarrow X) is an almost automorphic function, then x is a Stepanov-like almost automorphic function, that is, AA(mathbb{R}, X subset S^{p}AA(mathbb{R}, X).

Lemma 3.12 If φ ∈ PC ld ( T, X ) is an almost automorphic function with respect to the sequence T and { t k } ⊂ T is equipotentially almost automorphic satisfying inf i ∈ Z t i q = θ > 0, q ∈ Z, then { φ ( t k ) } is an almost automorphic sequence in X. Proof Let t i j = t i + j − t i, i, j ∈ Z. Obviously, from the definition of Π, it is easy to know that t i j ∈ Π.

We suppose that the linear part is the infinitesimal generator of a compact C0-semigroup of bounded linear operators and the nonlinear part is an almost automorphic function with respect to the second argument.

A function u ∈ B C 0 ( R, X ) is called an almost automorphic function (in the Bochner sense) when, for all real sequence ( s n ) n, there exists a subsequence ( t n ) n of ( s n ) n such that for all t ∈ R, lim n → ∞ u ( t + t n ) = v ( t ) exists in X, and for all t ∈ R, lim n → ∞ v ( t − t n ) = u ( t ) exists.