Spectral Properties of a Class of Generalized Landau Operators

摘要

We define and study some properties of operators formally given by [image omitted] In particular we show that when [image omitted] is essentially self-adjoint and the symbol a belongs to a certain Shubin class then the spectrum of [image omitted] is discrete and coincides with that of the usual Weyl operator A=aw(x, -ix). In addition, the eigenvalues of [image omitted] are in this case infinitely degenerate and the corresponding eigenfunctions can be obtained from those of A using a family of isometries L2 (n) L2(2n) indexed by the eigenfunctions of A.