Polynomial approximation on parabolic manifolds
Azimbay SadullaevNational University of Uzbekistan named after Mirzo Ulugbek, Tashkent, UzbekistanAlimardon Abdirimovich AtamuratovV. I. Romanovskiy Institute of Mathematics of the Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan
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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.
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