From 7a2346d3ee81c7c852de85527de056fe0b39aad8 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Thu, 19 Jan 2023 21:28:23 +0100
Subject: More improvements to knowledge base

---
 source/know/concept/parsevals-theorem/index.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

(limited to 'source/know/concept/parsevals-theorem/index.md')

diff --git a/source/know/concept/parsevals-theorem/index.md b/source/know/concept/parsevals-theorem/index.md
index 41e8fed..a7ce0bf 100644
--- a/source/know/concept/parsevals-theorem/index.md
+++ b/source/know/concept/parsevals-theorem/index.md
@@ -17,7 +17,7 @@ where $$A$$, $$B$$, and $$s$$ are constants from the FT's definition:
 $$\begin{aligned}
     \boxed{
         \begin{aligned}
-            \Inprod{f(x)}{g(x)} &= \frac{2 \pi B^2}{|s|} \inprod{\tilde{f}(k)}{\tilde{g}(k)}
+            \inprod{f(x)}{g(x)} &= \frac{2 \pi B^2}{|s|} \inprod{\tilde{f}(k)}{\tilde{g}(k)}
             \\
             \inprod{\tilde{f}(k)}{\tilde{g}(k)} &= \frac{2 \pi A^2}{|s|} \Inprod{f(x)}{g(x)}
         \end{aligned}
@@ -29,7 +29,7 @@ $$\begin{aligned}
 We insert the inverse FT into the definition of the inner product:
 
 $$\begin{aligned}
-    \Inprod{f}{g}
+    \inprod{f}{g}
     &= \int_{-\infty}^\infty \big( \hat{\mathcal{F}}^{-1}\{\tilde{f}(k)\}\big)^* \: \hat{\mathcal{F}}^{-1}\{\tilde{g}(k)\} \dd{x}
     \\
     &= B^2 \int
@@ -65,7 +65,7 @@ $$\begin{aligned}
     &= 2 \pi A^2 \iint f^*(x') \: g(x) \: \delta\big(s (x \!-\! x')\big) \dd{x'} \dd{x}
     \\
     &= \frac{2 \pi A^2}{|s|} \int_{-\infty}^\infty f^*(x) \: g(x) \dd{x}
-    = \frac{2 \pi A^2}{|s|} \Inprod{f}{g}
+    = \frac{2 \pi A^2}{|s|} \inprod{f}{g}
 \end{aligned}$$
 {% include proof/end.html id="proof-fourier" %}
 
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