Spectral theory for operator matrices related to models in mechanics
Carsten Trunk · Mathematical Notes · 2008
We derive various properties of the operator matrix where A 0 is a uniformly positive operator and A 0 −1/2 DA 0 −1/2 is a bounded nonnegative operator in a Hilbert space H. Such operator matrices are associated with second-order problems of the form $$ \ddot z(t) + A_0 z(t) + D\dot z(t) = 0 $$ , which are used as models for transverse motions of thin beams in the presence of damping.