The multivariate Müntz-Szasz problem in weighted Banach space on \(\mathbb{R}^n\) (Q1723896)

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