Premium
Left‐Definite Regular Hamiltonian Systems
Author(s) -
Krall Allan M.
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951740114
Subject(s) - mathematics , positive definite matrix , sobolev space , linear subspace , resolvent , hamiltonian (control theory) , pure mathematics , hilbert space , hamiltonian system , invariant subspace , mathematical analysis , eigenvalues and eigenvectors , mathematical optimization , physics , quantum mechanics
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 because of the new intricacies they expose, some of which have made it possible to go beyond fourth order scale problems. We explore the left definite Sobolev settings for such problems, which are in general subspaces determined by boundary conditions. We show that the Hamiltonian operator remains self‐adjoint, and inherits the same resolvent and spectral resolution from its original L 2 space when set in the left‐definite Sobolev space.