Continuity of the varisolvent Chebyshev operator
Charles B. Dunham · Bulletin of the American Mathematical Society · 1968
In this note we show that the Chebyshev operator T is continuous at all functions whose best approximations are of maximum degree.Let F be an approximating function unisolvent of variable degree on an interval [a, j8] and let the maximum degree of F be w.Let P be the parameter space of F. All functions considered will be continuous and for such functions we define the norm ||g|| = max{ \g(x)\:a£x£ #}.The Chebyshev problem is, for a given continuous function ƒ, to find an element T(J) ~F(A* t •), A*&P, for which