query: Cauchy Schwarz inequality for $\langle f,g\rangle = \int_0^1f(x)g(x)\mathrm{d}x$
positive_passages.docid: 144500
positive_passages.text: Cauchy-Schwarz inequality proof (but not the usual one)
negative_passages.docid: 86717
negative_passages.text: Completeness of $\langle \mathscr{C} [0, 1], \| \cdot \|_1 \rangle$
negative_passages.docid: 60946
negative_passages.text: Find the matrix of $\langle f, g \rangle = \displaystyle\int_0^1 f(t) g(t) \, \mathrm dt$ with respect to the basis $\{1,t,\dots,t^n\}$
negative_passages.docid: 27587
negative_passages.text: inequality on the unit disk
negative_passages.docid: 105141
negative_passages.text: $\mathbb R[x]/\langle x^2+1\rangle\simeq\mathbb C$ and $\mathbb R[x]/\langle x^2+1\rangle$ contains a zero of $x^2+1$
negative_passages.docid: 156803
negative_passages.text: Proving a corollary to Schwarz lemma
negative_passages.docid: 92056
negative_passages.text: An inequality on holomorphic functions
negative_passages.docid: 108560
negative_passages.text: Proof of a Gaussian Integral property
negative_passages.docid: 27347
negative_passages.text: Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.
negative_passages.docid: 43350
negative_passages.text: Schwarz's Lemma exercise
negative_passages.docid: 156599
negative_passages.text: Wirtinger Inequality: $\int_0^1 f'^2 \geq \pi^2 \int_0^1 f^2 $
negative_passages.docid: 110368
negative_passages.text: Prove the following integral inequality: $\int_{0}^{1}f(g(x))dx\le\int_{0}^{1}f(x)dx+\int_{0}^{1}g(x)dx$
negative_passages.docid: 158180
negative_passages.text: An inequality of $\int_0^1 |f(x)|dx$
negative_passages.docid: 115495
negative_passages.text: Prove $\int _0^\infty f^2 dx \leq \cdots $ for $f$ convex
negative_passages.docid: 60685
negative_passages.text: The vector space formed on C[0,1] and the norm $(\int_{0}^{1}|f(t)|^2 dt)^{1/2} $
negative_passages.docid: 93910
negative_passages.text: Equality in Cauchy-Schwarz Inequality implies linear dependence.
negative_passages.docid: 91117
negative_passages.text: Schwarz Lemma - like exercise