SOME REMARKS ON LEFT-DEFINITE HAMILTONIAN-SYSTEMS IN THE REGULAR CASE

It is the aim to confront recent considerations of A. M. KRALL On the left-definite spectral theory of regular Hamiltonian systems with the results of former research in this field. A short survey of the main s ources starting with the work of E. HOLDER in 1935 is given. After tha t the essential features of the left-definite S-hermitian theory, as i t was developed by SCHAFKE and SCHNEIDER in 1965, are presented for th e special case of the problems treated by KRALL, and an application to Sturm-Liouville equations is given. By comparing methods and assumpti ons of both theories, it is shown that the main result in KRALL's pape rs, a theorem on eigenfunction expansions, can be obtained under much weaker conditions. Especially one gets rid of the problem that the res trictions in the work of KRALL even exclude the classical polar case w hich builds the starting-point of the left-definite theory.