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The purpose of this paper is to give an extension of Müntz-Szasz theorems to multivariable weighted Banach space. Denote by { λ k = ( λ k 1 , λ k 2 , . . . , λ k n ) } k = 1 ∞ a sequence of real numbers in R + n . The completeness of monomials { t λ k } in C α is investigated, where C α is the weighted Banach spaces which consist of complex continuous functions f defined on R n with f ( t ) exp ( - α ( t ) ) vanishing at infinity in the uniform norm.

The Multivariate Müntz-Szasz Problem in Weighted Banach Space on R n