Sentence examples similar to constant analytic from inspiring English sources

Let (h z)=a_{n}z^{n}+a_{n+1}z^{n+1}+cdots) be a non-constant analytic function in (mathbb{U}).

If ϑ is a non-constant analytic function defined on the unit disk D such that ϑ(D) ⊂D, the composition operator Cϑ is the operator on the Hardy space H2 of the unit disk defined by Cϑf = f ∘ ϑ.

The little n th weighted space, denoted by ω μ, 0 n ( D ), is a closed subspace of ω μ n ( D ), consisting of those f for which lim ∣ z ∣ → 1 μ z ∣ f n z ∣ = 0. Let φ be a non-constant analytic self-map of D, u ( z ) ∈ H ( D ), and m ∈ ℕ.

For the case of D φ, u m : A α p → ω μ n, we have the following results: Theorem 1. Assume that p > 0, α > -1, n, m ∈ ℕ, μ is a weight on D, φ is a non-constant analytic self-map of D, and u ∈ H ( D ).

For the case of D φ, u m : A α p → ω μ, 0 ( n ), our main results are the following: Theorem 2. Assume that p > 0, α > -1, n, m ∈ ℕ, μ is a weight on D, φ is a non-constant analytic self-map of D, and u ∈ H ( D ).

Lemma 5. Suppose u ∈ H ( D ), p > 0, α > - 1, n, m ∈ ℕ and φ is a non-constant analytic self-map of D. Then the operator D φ, u m : A α p → ω μ n is compact if and only if D φ, u m : A α p → ω μ n is bounded and for any bounded sequence {f k }k∈ℕin A α p which converges to zero uniformly on compact subsets of D as k → ∞, we have D φ, u m f k → 0 in ω μ ( n ) as k → ∞.

We used a constant comparative analytic process to identify themes and their patterns in the narrative accounts collected.

From grounded theory we adopted the iterative and constant comparative analytic method [ 34], but with a more reflexive, hermeneutic approach to data interpretation [ 35].

However, it could be argued that reviewers should seek out primary studies containing contradictory concepts as part of the translation process, in line with the principles of the constant comparative analytic method in which disconfirming or contradictory cases are used to test emerging understandings of the data [ 14].

Thus, can be written as, where is a constant and is analytic on.

From this, can be written as (see [11, page 382]), where is a constant and is analytic on.