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...

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Bibliographic Details
Published inSbornik. Mathematics Vol. 215; no. 5; pp. 703 - 716
Main Authors Sadullaev, Azimbay Sadullaevich, Atamuratov, Alimardon Abdirimovich
Format Journal Article
LanguageEnglish
Published 2024
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Summary: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.
ISSN:1064-5616
1468-4802
DOI:10.4213/sm9895e