Fourier Analysis on the Boolean Hypercube via Hoeffding Functional Decomposition
arXiv:2510.07088v4 Announce Type: replace Abstract: Fourier analysis on the Boolean hypercube is fundamentally defined as the orthogonal decomposition of the space of pseudo-Boolean functions with respect to the uniform probability measure. In this work, we propose an ANOVA-based generalization of the Fourier decomposition on the Boolean hypercube endowed with any arbitrary probability measure. We provide an emph{explicit} decomposition basis which generalizes the Walsh-Hadamard (or parity functions) basis under any emph{arbitrary} probability measure on the Boolean hypercube. We formulate […]