LEFT-DEFINITE REGULAR HAMILTONIAN-SYSTEMS

Linear Hamiltonian systems allow us to generalize, as well as consider , self-adjoint problems of any even order. Such left-definite problems are interesting, not only because of the generalization, but also bec ause of the new intricacies they expose, some of which have made it po ssible to go beyond fourth order scale problems. We explore the left d efinite Sobolev settings for such problems, which are in general subsp aces determined by boundary conditions. We show that the Hamiltonian o perator remains self-adjoint, and inherits the same resolvent and spec tral resolution from its original L(2) space when set in the left-defi nite Sobolev space.