Spectral Self-Affine Measures on the Generalized Three Sierpinski Gasket (Analysis in Theory and Applications, 2017)
The self-affine measure $μ_{M,D}$ associated with an iterated function system$\{φ_{d} (x)=M^{-1}(x+d)\}_{d\in D}$ 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.
Keywords: Compatible pair; orthogonal exponentials; spectral measure.