The maximal range problem for a bounded domain Original Research Article

Let Ω⊂CΩ⊂C be a bounded domain such that 0∈Ω0∈Ω. Denote by View the MathML sourcePn,n∈N≔{1,2,…}, the set of all complex polynomials of degree at most nn. Let View the MathML sourcePn(Ω)≔{p∈Pn:p(0)=0,p(D)⊂Ω}, Turn MathJax on where View the MathML sourceD≔{z:|z|<1}. We relate the maximal polynomial range View the MathML sourceΩn≔⋃p∈Pn(Ω)p(D) Turn MathJax on to the geometry of ΩΩ.