52 citations · 130 across the 32 of their papers we have counts for
5 papers · 1 filter
A characterization of the Khavinson-Shapiro conjecture via Fischer operators
Hermann Render
The Khavinson-Shapiro conjecture states that ellipsoids are the only bounded domains in euclidean space satisfying the following property (KS): the solution of the Dirichlet proble…
The Khavinson-Shapiro conjecture for domains with a boundary consisting of algebraic hypersurfaces
Hermann Render
The Khavinson-Shapiro conjecture states that ellipsoids are the only bounded domains in euclidean space satisfying the following property (KS): the solution of the Dirichlet proble…
A symmetry property for polyharmonic functions vanishing on equidistant hyperplanes
Ognyan Kounchev, Hermann Render
Let be a polyharmonic function of order defined on the strip satisfying the growth condition $$ \sup_{t\in K}\lef…
A new cubature formula with weight functions on the disc, with error estimates
O. Kounchev, H. Render
We introduce a new type of cubature formula for the evaluation of an integral over the disk with respect to a weight function. The method is based on an analysis of the Fourier ser…
Discrete Hybrid Polyharmonic Cubature Formulas with weight on the disc. with error bounds
O. Kounchev, H. Render
This paper is a second part of our study of the Discrete Polyharmonic Cubature Formulas on the disc. It completes our study and provides a satisfactory cubature formula in terms of…