Polynomial approximation on parabolic manifolds

On a parabolic manifold polynomials are defined in terms of a special exhaustion function, and the problem of polynomial approximation of analytic functions is considered. An example of a parabolic manifold on which the class of polynomials consists of the constants alone is presented. On regularly parabolic manifolds, which possess a large reserve of polynomials, an analogue of the celebrated Bernstein–Walsh theorem is proved.
Bibliography: 28 titles.