Journal of Inequalities and Applications
Volume 4 (1999), Issue 4, Pages 301-314
doi:10.1155/S1025583499000417
On weighted positivity of ordinary differential operators
Department of Mathematics, Linköping University, Linköping S-581 83, Sweden
Received 20 October 1998; Revised 14 January 1999
Copyright © 1999 Stefan Eilertsen. 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.
Abstract
Some elliptic differential operators possess a weighted positivity property, where the
weight is a fundamental solution of the operator. This property has interesting applications to partial differential operators. The present paper is devoted to the property for ordinarydifferential operators.
It is shown that the operator (1−d2/dx2)m has the positivity property if and only if m=0,1,2,3, while there exist operators of arbitrary even order for which the positivity holds. Some necessary conditions for the property are given.