Spectral Properties of a Class of Generalized Landau Operators

Maurice A. de Gosson
2008 Communications in Partial Differential Equations  
We de...ne and study some properties of operators formally given by e A = a 1 2 x + i@y; 1 2 y i@x : In particular we show that when e A is essentially self-adjoint and the symbol a belongs to a certain Shubin class then the spectrum of e A is discrete and coincides with that of the usual Weyl operator A = a w (x; i@x). In addition, the eigenvalues of e A are in this case in...nitely degenerate and the corresponding eigenfunctions can be obtained from those of A using a family of isometries L 2
more » ... y of isometries L 2 (R n ) ! L 2 (R 2n ) indexed by the eigenfunctions of A. MSC [2000] : Primary 35S99, 35P05; Secondary 35S05, 45A75
doi:10.1080/03605300802501434 fatcat:ybz2rqgwvbcpvbha2oapwazxhe