Directional Chebyshev constants on the boundary
Volume 134 / 2025
                    
                    
                        Annales Polonici Mathematici 134 (2025), 49-65                    
                                        
                        MSC: Primary 32U20                    
                                        
                        DOI: 10.4064/ap240917-3-5                    
                                            
                            Published online: 16 June 2025                        
                                    
                                                Abstract
We prove results on the existence of limits in the definition of (weighted) directional Chebyshev constants at all points of the standard simplex $\Sigma \subset \mathbb R^d$ for (locally) regular compact sets $K\subset \mathbb C^d$.