Journal of Inequalities and Applications
Volume 4 (1999), Issue 1, Pages 57-81

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

Copyright © 1999 B. M. Brown et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.