Muntz-type theorem on the segments emerging from the origin

作者：Gao Zhiqiang; Deng Guantie^*

来源：Journal of Approximation Theory, 2008, 151(2): 181-185.

DOI：10.1016/j.jat.2007.09.008

• Muntz-type theorem
• dense
• lacunary polynomials

A necessary and Sufficient condition is obtained for the linear span of a system of monomials {z(lambda) : lambda is an element of Lambda} to be dense in the space of all continuous functions defined on the line segments emerging from the origin, where A is a set of nonnegative integers. The result is a generalization of the Muntz theorem to the segments emerging from the origin and ail extension of the Mergelyan theorem to lacunary polynomials.

• 单位
  北京师范大学