LAUSR

In this work, we study the spectral property of a class of self-affine measures μ M,D on R2 generated by an expanding real matrix M=diagρ1−1,ρ2−1 and a non-collinear integer digit set D={(0,0)t,(α1,α2)t,(β1,β2)t} with αi−2βi∉3Z , i = 1, 2. We give the sufficient and necessary conditions so that μ M,D becomes a spectral measure, i.e., there exists a countable subset Λ⊂R2 such that {e 2πi⟨λ,x⟩: λ ∈ Λ} forms an orthonormal basis for L 2(μ M,D ). This extends the results of Dai, Fu and Yan (2021 Appl. Comput. Harmon. Anal. 52 63–81) and Deng and Lau (2015 J. Funct. Anal. 269 1310–1326).