The theory of approximation of functions of a real variable had its origin
in the work of Chebyshev (Tchebycheff) and the well-known theorem of
Weierstrass on the approximations of continuous functions by
polynomials. In the earlier part of this century the theory was developed by,
among others, De la Vallee Poussin, Dunham Jackson and S. Bernstein,
the last of whom contributed to the subject over a period of more that
forty years. Many Russian mathematicians have worked in this field
in the last twenty years, and the books of Achiezer (Theory of
Approximation 1947) and Natanson (The Constructive Theory of Functions
1949) are well known in translation.** The present book, as well as dealing
with the classical theory, gives an account mainly of recent Russian work.
About half the papers cited in the bibliography (to which reference is
made throughout the book) were published between 1950 and 1959.