Spectrality of a Class of Self-Affine Measures with Prime Determinant

Abstract

We study the spectrality of a class of self-affine measures with prime determinant. Spectral measures are connected with fractal geometry that shows some kind of geometrical self-similarity under magnification. To make the self-affine measure becomes a spectral measure with lattice spectrum, we provide two new sufficient conditions related to the elements of digit set and zero set, respectively. The two sufficient conditions are more precise and easier to be verified as compared with the previous research. Moreover, these conditions offer a fresh perspective on a conjecture of Lagarias and Wang.

Keywords

• spectral measure
• prime number
• digit set
• lattice spectrum