Approximation theory concepts of smoothness are of global nature

摘要: The main goal of this note is to prove that, in general, the smoothness concepts derived from membership an approximation space, are global nature. To claim we show that if (C[a,b],{An}) scheme and (An) satisfies de La Vallee-Poussin Theorem, there very smooth functions (in classical sense) failing assumption just at one extreme point interval [a,b] but being continuous on such their sequence best uniform errors {E(f,An)} decays as slow want. We also a similar result holds true for multidimensional case.