An analytic study of functions defined on self-similar fractals (Q1174603)

The author considers a self-similar set \(E\subseteq\mathbb{R}^ n\) of Hausdorff dimension \(s\) such that the overlapping parts are of Hausdorff measure zero with respect to \(H^ s\). He defines a complete orthonormal function system \(\Phi\) of \(L^ 2(E,H^ s)\) and computes the Dirichlet kernel of \(\Phi\). Some results about Fourier coefficients with respect to \(\Phi\) and their calculation for some concrete functions are obtained. There are some connections with a paper of \textit{J. Kigami} [Japan J. Appl. Math. 6, No. 2, 259-290 (1989; Zbl 0686.31003)].