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)
On discrepancy theorems with applications to approximation theory
We give an overview on discrepancy theorems based on bounds of the logarithmic potential of signed measures. The results generalize well-known results of P. Erdős and P. Turán on the distribution of zeros of polynomials. Besides of new estimates for the zeros of orthogonal polynomials, we give further applications to approximation theory concerning the distribution of Fekete points, extreme points and zeros of polynomials of best uniform approximation.
On existence in the Cauchy problem for the biharmonic equation