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Bound on L2-Norm of Probability Distributions?
I am working on a problem where I have continuous probability distributions $p$ over a bounded domain $D$, i.e., $\forall x$ $p(x) \geq 0$ and $\|p\|_1 = \int_D p(x) dx = 1$. However, I also want $p$ ...
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Coercive bilinear form for maximum norm
Let $f$ be a differentiable function. Denote a bilinear form by $$b(f,f) = \int_{0}^{1} \bigg( \frac{d f(x)}{dx} \bigg)^{2} dx.$$ Given $f(0) = 0,$ we want to show that $$a \cdot b(f,f) \geq ||f||_{\...
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