O zonální funkci harmonické
Old and new order of linear invariant family of harmonic mappings and the bound for Jacobian
The relation between the Jacobian and the orders of a linear invariant family of locally univalent harmonic mapping in the plane is studied. The new order (called the strong order) of a linear invariant family is defined and the relations between order and strong order are established.
On a boundary value problem for the heat equation
On a generalized asymptotic mean value property.
On a generalized logarithmic kernel and its potentials
On a generalized reflection law for functions satisfying the Helmholtz equation.
On a heat potential
On a heat potential (Preliminary communication)
On a potential problem with incident wave as a field source
On a question of T. Sheil-Small regarding valency of harmonic maps
The aim of this work is to answer positively a more general question than the following which is due to T. Sheil-Small: Does the harmonic extension in the open unit disc of a mapping f from the unit circle into itself of the form f(eit) = eiϕ(t), 0 ≤ t ≤ 2π, where ϕ is a continuously non-decreasing function that satisfies ϕ(2π)−ϕ(0) = 2Nπ, assume every value finitely many times in the disc?
On a result by Clunie and Sheil-Small
In 1984 J. Clunie and T. Sheil-Small proved ([2, Corollary 5.8]) that for any complex-valued and sense-preserving injective harmonic mapping F in the unit disk D, if F(D) is a convex domain, then the inequality |G(z2)− G(z1)| < |H(z2) − H(z1)| holds for all distinct points z1, z2∈ D. Here H and G are holomorphic mappings in D determined by F = H + Ḡ, up to a constant function. We extend this inequality by replacing the unit disk by an arbitrary nonempty domain Ω in ℂ and improve it provided F...
On a subclass of harmonic univalent functions.
On a theorem of Beardon and Maskit.
On a theorem of M. G. Arsove
On an extension of the definition of transfinite diameter and some applications.
On boundary integral equations of the first kind for the bi-laplacian in a polygonal plane domain
On certain harmonic measures on the unit disk
On certain p-harmonic functions in the plane.
On convergence sets of divergent power series
A nonlinear generalization of convergence sets of formal power series, in the sense of Abhyankar-Moh [J. Reine Angew. Math. 241 (1970)], is introduced. Given a family of analytic curves in ℂ × ℂⁿ passing through the origin, of a formal power series f(y,t,x) ∈ ℂ[[y,t,x]] is defined to be the set of all s ∈ ℂ for which the power series converges as a series in (t,x). We prove that for a subset E ⊂ ℂ there exists a divergent formal power series f(y,t,x) ∈ ℂ[[y,t,x]] such that if and only if...
On cyclic and radial variations of a plane path (Preliminary communication)