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Let $q(x)$ be a probability density function over $[0,1]$. Let $\lambda > 0$ and $f: [0,1] \to \mathbb{R}$ be any solution to the following ODE: $$ \lambda f''(x) + q(x) f(x) = 0, \text{for all }x \...

At the moment, I don't have access to the early 1960's paper of John and Nirenberg that (from what I understand) introduced the space BMO (bounded mean oscillation). Why were John and Nirenberg ...