36 citations · 52 across the 16 of their papers we have counts for
16 papers
The Complex Green's Function for Symmetric Sets
Klaus Schiefermayr, Olivier Sète
The aim of this paper is threefold: (i) We study the complex Green's function (the analytic extension of the real Green's function) for multiply connected domains with some symmetr…
Weighted Chebyshev Polynomials on Compact Subsets of the Complex Plane
Galen Novello, Klaus Schiefermayr, Maxim Zinchenko
We study weighted Chebyshev polynomials on compact subsets of the complex plane with respect to a bounded weight function. We establish existence and uniqueness of weighted Chebysh…
Walsh's Conformal Map onto Lemniscatic Domains for Several Intervals
Klaus Schiefermayr, Olivier Sète
We consider Walsh's conformal map from the complement of a compact set with components onto a lemniscatic domain …
Walsh's Conformal Map onto Lemniscatic Domains for Polynomial Pre-images II
Klaus Schiefermayr, Olivier Sète
We consider Walsh's conformal map from the exterior of a set consisting of compact disjoint components onto a lemniscatic domain. In particular, w…
Walsh's conformal map onto lemniscatic domains for polynomial pre-images I
Klaus Schiefermayr, Olivier Sète
We consider Walsh's conformal map from the exterior of a compact set onto a lemniscatic domain. If is simply connected, the lemniscatic domain is the e…
Some new properties of Jacobi's theta functions
Klaus Schiefermayr
In this paper, a monotonicity property for the quotient of two Jacobi's theta functions with respect to the modulus is proved.
Inverse polynomial images which consists of two Jordan arcs - An algebraic solution
Klaus Schiefermayr
Inverse polynomial images of , which consists of two Jordan arcs, are characterised by an explicit polynomial equation for the four endpoints of the arcs.
An upper bound for the logarithmic capacity of two intervals
Klaus Schiefermayr
The logarithmic capacity (also called Chebyshev constant or transfinite diameter) of two real intervals has been given explicitly with the help of Jacobi's ellipt…
A lower bound for the minimum deviation of the Chebyshev polynomial on a compact real set
Klaus Schiefermayr
In this paper, we give a sharp lower bound for the minimum deviation of the Chebyshev polynomial on a compact subset of the real line in terms of the corresponding logarithmic capa…
Inverse polynomial images consisting of an interval and an arc
Klaus Schiefermayr
In this paper, some geometric properties of inverse polynomial images which consist of a real interval and an arc symmetric with respect to the real line are obtained. The proofs a…
The Polya-Chebotarev problem and inverse polynomial images
Klaus Schiefermayr
Consider the problem, usually called the Pólya-Chebotarev problem, of finding a continuum in the complex plane including some given points such that the logarithmic capacity of thi…
A density result concerning inverse polynomial images
Klaus Schiefermayr
In this paper, we consider polynomials of degree , for which the inverse image of consists of two Jordan arcs. We prove that the four endpoints of these arcs form an ${…
Inequalities for the Jacobian elliptic functions with complex modulus
Klaus Schiefermayr
Despite the fact that there is a huge amount on papers and books devoted to the theory of Jacobian elliptic functions, very little is known when the modulus of these functions…
Geometric properties of inverse polynomial images
Klaus Schiefermayr
Given a polynomial $\T_n$ of degree , consider the inverse image of and , denoted by $\T_n^{-1}(\R)$ and $\T_n^{-1}([-1,1])$, respectively. It is well known that $\…
A lower bound for the norm of the minimal residual polynomial
Klaus Schiefermayr
Let be a compact infinite set in the complex plane with , and let be the minimal residual polynomial on , i.e., the minimal polynomial of degree at most $n…
Estimates for the asymptotic convergence factor of two intervals
Klaus Schiefermayr
Let be the union of two real intervals not containing zero. Then denotes the supremum norm of that polynomial of degree less than or equal to , which is min…