Asymptotic behavior of the Weyl function of the Sturm-Liouville operator (Q1358414)

The Weyl function \(m(\lambda)\) of the Sturm-Liouville operator determined by the problem \(-y''+ q(x)y=\lambda y\), \(y'(0)- hy(0)= 0\) is investigated. By studying the singularities of the weighted zeta function, the author discusses the asymptotic behavior of \(m(\lambda)\) as \(\lambda\) tends to \(\infty\) and \(\delta<\arg\lambda<\pi-\delta\), for some \(\delta>0\).