Nonspectrality of Certain Self-Affine Measures on ℝ3 - Gui-Bao Gao (Abstract and Applied Analysis)
We will determine the nonspectrality of self-affine measure μB,D corresponding to B=diag[p1,p2,p3]  (p1∈(2ℤ+1)∖{±1}, p2∈2ℤ∖{0}), and D={0,e1,e2,e3} in the space ℝ3 is supported on T(B,D), where e1,  e2, and e3 are the standard basis of unit column vectors in ℝ3, and there exist at most 4 mutually orthogonal exponential functions in L2(μB,D), where the number 4 is the best. This generalizes the known results on the spectrality of self-affine measures.