(untitled) (Analysis in Theory and Applications, 2017)
The self-affine measure μ_M,D associated with an iterated function system{φ_d (x)=M^-1(x+d)}_dD is uniquely determined. It only depends upon an expanding matrix M and a finite digit set D. In the present paper we give some sufficient conditions for finite and infinite families of orthogonal exponentials. Such research is necessary to further understand the non-spectral and spectral of μ_M,D. As an application, we show that the L^2(μ_M, D) space has infinite families of orthogonal exponentials on the generalized three Sierpinski gasket. We then consider the spectra of a class of self-affine measures which extends several known conclusions in a simple manner.