Kernels of linear maps

The theorem of Duistermaat and Van der Kallen from 1998 proved the first case of the Mathieu conjecture. Using the theory of Mathieu-Zhao spaces, we can reformulate this theorem as Ker L is a Mathieu-Zhao space where L is the linear map L : C [ X 1 , … , X n , X 1 − 1 , … , X n − 1 ] → C , f ↦ f 0 . In this paper, we generalize this result (for n = 1 ) to all non-trivial linear maps L : C [ X , X − 1 ] → C such that { X n | | n | ≥ N } ⊂ Ker L for some N ≥ 1 .