The HELP inequality for Hamiltonian systems

Abstract

We extend the Hardy–Everitt–Littlewood–Polya inequality, hitherto established for 2nth order formally selfadjoint ordinary differential equations, to a wide class of linear Hamiltonian systems. The method follows Dias (Ph.D. thesis, Cardiff: University of Wales, 1994) but without the Hilbert space setting which he uses.

Keywords

• Hardy
• Everitt
• Littlewood
• Polya
• Hamiltonian system
• Inequality