FreiesMathe
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- Dec 13, 2015
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Hello, we had a task and solved it, but we aren't sure if it's correct like this. It'd be great if someone could help us c:
Given two functions \(\displaystyle f,g \in L^2(\mathbb{R}^d) \). Is the following estimation correct?
\(\displaystyle (f*g)(x) = \int_{\mathbb{R}^d} f(x-y)g(y) \, \mathrm{d}y = \text{||} fg \text{||}_1 \le \text{||} f \text{||}_2 \text{||} g \text{||}_2 \)
We used Hölder's inequality for this.
Thanks for your help
Given two functions \(\displaystyle f,g \in L^2(\mathbb{R}^d) \). Is the following estimation correct?
\(\displaystyle (f*g)(x) = \int_{\mathbb{R}^d} f(x-y)g(y) \, \mathrm{d}y = \text{||} fg \text{||}_1 \le \text{||} f \text{||}_2 \text{||} g \text{||}_2 \)
We used Hölder's inequality for this.
Thanks for your help