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We prove that the abscissas of Bohr and Rogosinski for ordinary Dirichlet series, mapping the right half-plane into the bounded convex domain G ⊂ ℂ are independent of the domain G. Furthermore, we obtain new estimates about these abscissas.
Jacobi’s elliptic integrals and elliptic functions arise naturally from the Schwarz-Christoffel conformal transformation of the upper half plane onto a rectangle. In this paper we study generalized elliptic integrals which arise from the analogous mapping of the upper half plane onto a...
Let μ be a locally finite complex valued measure on ℂ with an angular density with respect to a proximate order ρ(r) and let $$ be the canonical Cauchy potential of μ. The main part of this paper is devoted to an estimate of f μ (reiø) uniformly in ø generalising some results of A. Gol’dberg, N....
Let k ∈ ℕ and let A, B be finite subsets of ℂ. Under appropriate conditions on k, A and B we determine those entire functions f such that f (z) ∈ A implies that f(k)(z) ∈ B.
In this article, we improve results of Langley and Whitehead on Bank-Laine functions. If E is a Bank-Laine function and F is an entire function of finite order which has the same zeros as E in a certain sector S of the complex plane and the set of Bank-Laine points of F in S has positive lower...
We study the geometry of the space of all non-empty subsets of the real line ℝ of cardinality at most three endowed with the Hausdorff metric. The space is known to be homeomorphic to the 3-dimensional Euclidean space ℝ3. We prove that it is, in fact, (3 + 4π)-bi-Lipschitz equivalent to ℝ3. We...
We show how to express a conformal map Φ of a general two-connected domain in the plane, such that neither boundary component is a point, onto a representative domain of the form...
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