Müntz-type theorem on the segments emerging from the origin

  • Authors:

  • Zhiqiang Gao;Guantie Deng

  • Affiliations:

  • School of Mathematical Sciences, Beijing Normal University, Beijing 100875, The People's Republic of China and L.M.A.M., Université de Bretagne Sud, campus de Tohannic, BP 573, 56017 Vannes, ...;School of Mathematical Sciences, Beijing Normal University, Beijing 100875, The People's Republic of China

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2008

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Abstract

A necessary and sufficient condition is obtained for the linear span of a system of monomials {z^@l:@l@?@L} to be dense in the space of all continuous functions defined on the line segments emerging from the origin, where @L is a set of nonnegative integers. The result is a generalization of the Muntz theorem to the segments emerging from the origin and an extension of the Mergelyan theorem to lacunary polynomials.