Harmonic analysis of fractal measures induced by representations of a certain C${}^{\ast }$-algebra

Palle E. T. Jorgensen, Steen Pedersen

We describe a class of measurable subsets $\Omega$ in $\br^d$ such that $L^2(\Omega )$ has an orthogonal basis of frequencies $e_{\lambda }(x)=e^{i2\pi \lambda \cdot x}(x\in \Omega )$ indexed by $λ\inΛ\subset\br^d$. W…