Full Müntz theorem in \(L_ p[0,1]\) (Q1914807)

The author proves the following theorem, conjectured by P. Borwein and T. Erdélyi: Let \(1< p< \infty\) and \(\{\lambda_i \}^\infty_0\) be a sequence of distinct real numbers greater than \(-1/p\). Then the linear span of the functions \(\{x^{\lambda_i} \}_0^\infty\) is dense in \(L_p [0, 1]\) if and only if \[ \sum^\infty_{i=0} {{\lambda_i+ 1/p} \over {(\lambda_i+ 1/p)^2+ 1}}= \infty. \]