One-dimensional Schr\"odinger operators with $\delta'$-interactions on a   set of Lebesgue measure zero
  We give an abstract definition of a one-dimensional Schr\"odinger   operator with $\delta'$-interaction on an arbitrary set~$\Gamma$ of   Lebesgue measure zero. The number of negative eigenvalues of such an   operator is at least as large as the number of those isolated points   of the set~$\Gamma$ that have negative values of the intensity   constants of the $\delta'$-interaction. In the case where the   set~$\Gamma$ is endowed with a Radon measure, we give constructive   examples of such operators having an infinite number of negative eigenvalues. 
Johannes F. Brasche and Leonid Nizhnik
math.FA math.SP