On the spectra of Sierpinski-type self-affine measures (Q279777)

Let \(\mu\) be a probability measure with compact support on \({\mathbb R}^2\). Its spectrum is a discrete set \(\Lambda\subset {\mathbb R}^2\) such that \(E_{\Lambda}:= \{\exp 2\pi i(\xi, \lambda): \lambda\in\Lambda\}\) is an orthogonal basis of \(L^{2}(\mu)\). The author studies the spectra of Sierpinski-type self-affine measures. In particular, he finds conditions on a given set \(\Lambda\) under which it is the spectrum of measures of this type.