Sentence examples for be the open unit from inspiring English sources

Let (B_n) be the open unit ball in (mathbb {C}^n).

Let D be the open unit disk in the complex plane.

Let Ω = ( 0, 1 ) 3 ⊂ R 3 be the open unit cube.

Let D : = { z ∈ ℂ : ∣ z ∣ < 1 } be the open unit disk in the complex plane ℂ.

Let D = { z ∣ | z | < 1 } be the open unit disc in the complex plane ℂ.

Let be the open unit disk in the complex plane and let be an analytic self-map of.

In particular, we obtain many results when X=Δ where Δ is the open unit disc.

When Ω is the open unit disk D and certain natural additional hypotheses are added we call such kernels k Bergman-type kernels.

If B is the open unit ball of a strictly convex Banach space (X, ‖·‖) and f: B→B is holomorphic, condensing with respect to α‖·‖, and fixed-point-free, then there exists ξ∈∂B such that the sequence lcub;fn} of the iterates of f converges in the compact-open topology to the constant map taking the value ξ.

where U is the open unit disk U = { z ∈ ℂ : | z | < 1 }.

where U = { z : | z | < 1 } is the open unit disk and f is analytic in U satisfying the Riemann mapping conditions.