Spectrality of generalized Sierpinski-type self-affine measures

In this work, we study the spectral property of generalized Sierpinski-type self-affine measures μ M , D on R 2 generated by an expanding integer matrix ∈ ( Z ) with det ⁡ 3 and a non-collinear digit set = { 0 t α 1 β } − . We give sufficient necessary conditions for to be measure, i.e., there exists countable subset Λ ⊂ such that E e π i 〈 λ x 〉 : forms orthonormal basis L This completely settles spectrality measure