ASYMPTOTICS OF DIRICHLET SPECTRUM ON SOME CLASS OF NONCOMPACT DOMAINS

We investigate the asymptotic behaviour of the counting function of Di richlet eigenvalues on some class of noncompact manifolds. We prove th at in cases when the volume or the perimeter (the volume of the bounda ry) of the manifold is infinite, some additional (nonclassical) terms appear in the precise asymptotics. The coefficients at the classical t erms in those are regularized in some special way volume (resp. perime ter) of the manifold.