FOURIER BASES OF A CLASS OF PLANAR SELF-AFFINE MEASURES

Let mu M,D be the planar self-affine measure generated by an expansive integer matrix M is an element of M2(1) and a noncollinear integer digit set We show that mu M,D is a spectral measure if and only if there exists a matrix Q is an element of M2(R) such that ( similar to M, D similar to) is admissible, where M similar to = QMQ-1 and D similar to = Q D. In particular, when alpha 1 beta 2 -alpha 2 beta 1 is an element of/271, mu M,D is a spectral measure if and only if M is an element of M2(271). This completely settles the spectrality of the self-affine measure mu M,D.