Spectrality of a class of self-affine measures on * *The research is supported in part by the NNSF of China (Nos. 12071125, 11971500, 11831007 and 11771457), the Hunan Provincial NSF (No. 2019JJ20012).

Abstract

In this work, we study the spectral property of a class of self-affine measures μ M,D on generated by an expanding real matrix and a non-collinear integer digit set with , 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 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).