From basic
logic to axiomatic Set Theory. Curiously, set theory arose in the context of
sets of real numbers related to the convergence of Fourier series...In 1829, Dirichlet had shown that a function always had a Fourier series converging to itself, under certain sufficient conditions (he considered periodic functions with finitely many extrema in every period and equal to the half-sum of ... We prove a strong maximum principle for Schr\"odinger operators defined on a class of fractal
sets and their blowups without boundary. Our primary interest is in weaker regularity conditions than have previously appeared in the literature; in particular we permit both the fractal Laplacian and the potential to be Radon measures on the fractal.
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