Schrödinger Operators, Spectral Analysis and Number Theory

We study bounded trace maps on hypersurfaces for Sobolev spaces from a point of view that is fundamentally different the one in classical theory. This allows us to construct under weak regularity assumptions hypersurfaces. In case domains $\mathbf R^n$ we only require continuity boundary. For whole space assume are Lebesgue measurable. As an application our consider Dirichlet problem and prove coarea formula where level sets assumed be measurable