The Estimation of Lower Bound for Fourier Change of One Self-affine Measure in R~3
Zhang Long-sheng · Journal of China West Normal University · 2010
Singularity is an important property of measure.The relationship between the lower bound of the sequence {|μλ,D,W(αk)|}∞k =0 and the singularity of the self-affine measure μλ,D is very close.In this paper,we will prove that there exists a positive lower bound for the sequence {|μλ,D,W(αk)|}∞k =0 in the general directions to infinity in R3,and then prove that self-affine measure μλ,D is singular.