Indian Journal of Science and Technology

Abstract

Background: Elliptic differential operators and asymptotic distribution of eigenvaluesof them are discussed in many works. Methods: In this paper we get some new results about an important differential operator on a Hilbert space. Also asymptotic distribution of eigenvalues of this kind of differential operators are proved with new methods that estimation of the resolvent of the operators is used in this paper. Finding: We get some new theorems about the differential operator A.We consider a bounded domain Ω with smooth boundary in R^n define a norm and find the asymptotic distribution of eigenvalues of the operator ( ) , 2 , , 1 ( )( ) () ()() () i j n a i j ij x x Au x p x a x q x u x =−∑ = in the space 2 ( )l H L l = Ω . Improvement: We improve the methodof proving this kind of theorems.

Keywords: Asymptotic Distribution, Eigenvalues, Non-SelfAdjoint Elliptic Differential Operator, Resolvent