International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 47-68
doi:10.1155/S0161171298000064

Relatively bounded and compact perturbations of nth order differential operators

Abstract

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.