We consider a smooth submanifold N with a smooth boundary in an ambient closed manifold M and assign a spectral invariant c(α,H) to every singular homological class α∈H∗(N) and a Hamiltonian H defined on the cotangent bundle T∗M. We also derive certain properties of spectral numbers, for example we prove that spectral invariants c±(H,N) associated to the whole Floer homology HF∗(H,N:M) of the submanifold N, are the limits of decreasing nested family of open sets