Estimates for the eigenfunctions of the Regge problem (Q1938638)

Consider the eigenvalue problem \[ \begin{gathered} -y''(x)+ q(x) y(x)= \lambda^2\rho(x) y(x),\quad 0< x< a,\\ y(0)= 0,\quad y'(a)- i\lambda y(a)= 0\end{gathered}\tag{\(*\)} \] under the assumptions that the functions \(q\) and \(\rho\) are integrable on \([0,a]\) and nonnegative. The authors derive results on the growth of the norm of the eigenfunctions of \((*)\) under the normalization condition \[ \int^a_0 \rho(x)|y(x)|^2 dx= 1. \]