Eigenvalues associated with Borel sets.

Abstract

Every Borel subset $K$ of an interval $[c,d]$ induces a sequence of eigenvalues. If $K$ is closed, the asymptotic behavior of the eigenvalues is related to the positions and lengths of its complementary intervals. The rate of growth becomes ``lowest possible'' if $K$ has self-similarity properties. Eigenvalues of a vibrating string with singular mass distribution are eigenvalues associated with a set $K$.