Constraints on the induced gravitational wave background from primordial
  black holes
  We perform a consistent calculation of primordial black hole (PBH) mass
spectrum and second-order induced gravitational wave (GW) background produced
from primordial scalar perturbations in radiation era of the early Universe. It
is shown that the maximal amplitudes of the second order GW spectrum that can
be approached without conflicting with the PBH data do not depend significantly
on the shape of primordial perturbation spectrum. The constraints on the GW
background obtained in previous works are extended to a wider GW frequency
range. We discuss the applicability of the currently available pulsar timing
limits for obtaining the constraints on scalar power spectrum and PBH abundance
and show that they can be used for strongly constraining the PBH number density
in the PBH mass range $\sim (0.03 - 10) M_{\odot}$.
