52 citations · 130 across the 32 of their papers we have counts for
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Dirichlet's problem with entire data posed on an ellipsoidal cylinder
Dmitry Khavinson, Erik Lundberg, Hermann Render
We consider the Dirichlet problem in an ellipsoidal cylinder when the data function is entire. Under an additional assumption that the order of the data function is less than one,…
The Dirichlet problem for the slab with entire data and a difference equation for harmonic functions
Dmitry Khavinson, Erik Lundberg, Hermann Render
It is shown that the Dirichlet problem for the slab with entire boundary data has an entire solution. The proof is based on a generalized Schwarz refl…
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…
Polyharmonic functions of infinite order on annular regions
Ognyan Kounchev, Hermann Render
Polyharmonic functions f of infinite order and type τ on annular regions are systematically studied. The first main result states that the Fourier-Laplace coefficients f_{k,l}(r) o…