Sentence examples for be a holomorphic self-map from inspiring English sources

Let be a holomorphic self-map of and.

Let be a holomorphic self-map and let be a holomorphic function on the unit ball.

Corollary 4. Let φ = (φ1,..., φ n ) be a holomorphic self-map of U n and α > 0. Then the following are equivalent.

The following corollary is obtained immediately from Theorem 1. Corollary 2. Let φ = (φ 1,..., φ n ) be a holomorphic self-map of U n and α > 0.

Let 0 < α, β < ∞, m be a nonnegative integer and φ be a holomorphic self-map of the unit disk D. Suppose that C φ D m : B α → B β is bounded.

For (alpha>-1), let φ be a holomorphic self-map of D and u a non-negative, bounded, and measurable function on D. Define the measure (u {lambda}_{alpha}) by (u{lambda}_{alpha}(E)) (:= int_{E}u z), d {lambda}_{alpha} z)) on all Borel subsets (Esubseteqmathbf{D}).

Assume that, is a holomorphic self-map of and is a weight.

Suppose ψ is a holomorphic self-map of U that is not an elliptic automorphism.

Assume that, or and,, is a weight, and is a holomorphic self-map of, and is bounded.

Assume that, or and,, is a weight, and is a holomorphic self-map of Then is bounded if and only if and condition (3.2) holds.

Suppose that ψ is a holomorphic self-map of U such that ||ψ|| U < 1, and the composition operator C ψ acts boundedly on a Banach space of formal power series H p with.