International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 47-68

Relatively bounded and compact perturbations of nth order differential operators

Terry G. Anderson

Department of Mathematical Sciences, Appalachian State University, Boone 28608, NC, USA

Received 10 June 1996; Revised 26 August 1996

Copyright © 1998 Terry G. Anderson. 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.


A perturbation theory for nth order differential operators is developed. For certain classes of operators L, necessary and sufficient conditions are obtained for a perturbing operator B to be relatively bounded or relatively compact with respect to L. These perturbation conditions involve explicit integral averages of the coefficients of B. The proofs involve interpolation inequalities.