Spectral asymptotics of nonself-adjoint elliptic differential operators in the whole space (Q1386606)

We consider the differential operator \[ {\mathcal P} u=\sum_{| \alpha|= | \beta |\in J} D^\alpha \bigl(\langle x \rangle^{\theta_{| \alpha|}} a_{\alpha \beta} (x) D^\beta u(x) \bigr), \quad D({\mathcal P}) =C^\infty_0 (\mathbb{R}^n) \] in the space \(L_2 (\mathbb{R}^n)\). Here, \(\langle x\rangle =(1+| x|^2)^{1/2}\), \(D= (\partial/i \partial x_1), \dots, \partial/i \partial x_n)\), \(J\) is a finite set of nonnegative integers. This work deals with the study of the asymptotics of the spectrum of this nonselfadjoint operator.