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).
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