virial theorem, C0- semigroups, One-parameter semigroups and linear evolution equations, \(C_{0}\)-semigroups, boundary values of resolvent families, Applications of operator theory in the physical sciences, resolvent estimates, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, positive commutators, Mourre estimate, conjugate operators, Resolvent estimates, Positive commutators, Scattering theory for PDEs, Commutators, derivations, elementary operators, etc., Boundary values of resolvent families, Conjugate operator, Virial theorem, Analysis, Selfadjoint operator theory in quantum theory, including spectral analysis