Sentence examples for absolute uniform from inspiring English sources

Consequently, the absolute uniform convergence of the series in (5.3) on I implies that ϕ k ( t ) converges uniformly to some function ϕ ( t ) on I. Our objective now is to show that ϕ ( t ) is a solution of (4.1) for all t ∈ I. From the Lipschitz condition ∥ f ( t, ϕ ( t ) ) − f ( t, ϕ m ( t ) ) ∥ ≤ A ∥ ϕ ( t ) − ϕ m ( t ) ∥. for all t ∈ [ θ, θ + a ].

where the convergence is absolute and uniform on ℝ and it is uniform on compact sets of ℂ, cf. [6 8].

The absolute and uniform convergence of the series ((S_1f)(t)) follows from Lemma 3.

The proof of absolute and uniform convergence of the series (3.4) is analogous.

The absolute and uniform convergence of the series (3.9) and (3.10) in Ω̅ follows from Lemmas 3.1-3.5 3.1-3.5

The absolute and uniform convergence of the series (3.11) in Ω̅ follows from the Lemmas 3.2, 3.5, 3.7, and 3.8.

will enable us to show absolute and uniform convergence of practically all series considered in the sequel.

The absolute and uniform convergence of the series (3.8) in Ω̅ follows from Lemma 3.3 with (m=k ) and from Lemmas 3.4 and 3.5.

The same estimate holds for the space (C mathbb {R})), giving the absolute and uniform convergence of ((S_{1,n}f)(t)) to ((S_1f)(t)).

Then f ^ λ = ∑ n = - ∞ ∞ f ^ λ n S n λ. with absolute convergence, uniform on strips of finite width in ℂ around ℝ. If we substitute the expression (30) in (3: 2) we obtain f ^ λ = ∫ - π π V f θ e - i λ θ d θ, (40).

In 1963, Yu [4] proved the Valiron-Knopp-Bohr formula of the associated abscissas of bounded convergence, absolute convergence and uniform convergence of Laplace-Stieltjes.