The discreteness of spectrum for higher-order differential operators in the weighted function spaces

Abstract

In this paper we consider the discreteness of spectrum for higher-order differential operators in the weighted function spaces. Using the method of the embedding theorems of weighted Sobolev spaces $H_p^n$ in weighted spaces $L_{s,r}$, we obtain a new sufficient and necessary condition to ensure that the spectrum is discrete, which can be easily used to judge the discreteness of some differential operators. 10.1017/S000497271200068