Convergence of mock Fourier series

For certain Cantor measures μ on ℝn, it was shown by Jorgensen and Pedersen that there exists an orthonormal basis of exponentialse2πiγ·x for λεΛ. a discrete subset of ℝn called aspectrum for μ. For anyL1 functionf, we define coefficientscγ(f)=∝f(y)e−2πiγiydμ(y) and form the Mock Fourier series ∑λ∈Λcλ(f)e2πiλ·x. There is a natural sequence of finite subsets Λn increasing to Λ asn→∞, and we define the partial sums of the Mock Fourier series by\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$s_n (f)(x) = \sum\limits_{\lambda \in \Lambda _n } {c_n (f)e^{2\pi i\lambda \cdot x} } .$$ \end{document}