Journal of Inequalities and Applications 
Volume 4 (1999), Issue 1, Pages 57-81
doi:10.1155/S1025583499000296

The HELP inequality for Hamiltonian systems

B. M. Brown,1 W. D. Evans,2 and M. Marletta3

 1Department of Computer Science, University of Wales, Cardiff, PO Box 916, Cardiff CF2 3XF, UK
2School of Mathematics, University of Wales, Cardiff, Senghennydd Road, Cardiff CF2 4YH, UK
3Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester LE1 7RH, UK
Received 30 July 1998; Revised 15 September 1998

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.