Integral estimates for the distribution of the spectrum of a string (Q1088827)

Let \(\lambda_ n\) be eigenvalues of the singular string located at the interval \(J\subset {\mathbb{R}}\) and characterized by the mass distribution M(x). Sufficient (and sometimes necessary) conditions on M(x) are given ensuring that \(\sum \lambda_ n^{-\alpha}<\infty\), \(\alpha\in (0,1)\).