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- PublicationThe Dirichlet problem for the slab with entire data and a difference equation for harmonic functionsIt is shown that the Dirichlet problem for the slab (a,b)×Rd with entire boundary data has an entire solution. The proof is based on a generalized Schwarz reflection principle. Moreover, it is shown that for a given entire harmonic function g the inhomogeneous difference equation h(t+1,y)−h(t,y)=g(t,y) has an entire harmonic solution h.
221Scopus© Citations 4
- PublicationBoundary behaviour of universal Taylor seriesA power series that converges on the unit disc D is called universal if its partial sums approx- imate arbitrary polynomials on arbitrary compacta in CnD that have connected complement. This paper shows that such series grow strongly and possess a Picard-type property near each boundary point.
365Scopus© Citations 9