Source: If $f \in L^2$ , then $\hat{f} \in L^2$ and $2\pi ||f||_{L^2} = ||\hat{f}||_{L^2}$, where $\hat{f}$ is the fourier transform
97917
Step in the Stein's proof of Plancherel Theorem
63453
A proof of the fact that the Fourier transform is not surjective from $\mathcal{L}^1(\mathbb{R})$ to $C_0( \mathbb{R})$
100608
Prove that $\|v\|_{H^1(\Omega )}\leq C(\|f\|_{L^2(\Omega )}+\|v\|_{H^{1/2}(\partial \Omega )}+\|\partial _\nu v\|_{H^{1/2}(\partial \Omega )}))$
20025
Fourier transform of $\exp(-t^2)$ using contour integration.
79132
Fourier transform of modified Bessel function of the second kind
105790
What is the Fourier Transform of $f'(x)/x$
133851
How to arrive at $\int_{0}^{1} f^3(x) \, dx < (\int_{0}^{1} f(x) \, dx)^2$?
147606
If $f^2$ is Riemann Integrable is $f$ always Riemann Integrable?
134043
Prove that for $ f(x+2\cdot\pi)=f(x), x \in \mathbb{R} $, there exists $ x_0 $ so $ f(x_0+\pi)=f(x_0) $
10675
Proving that $\frac{1}{2\pi}\int_{0}^{2\pi}|f(re^{it})|^2dt=\sum_{n=0}^{\infty}|a_n|^2r^{2n}$
123799
Calculating the Fourier transform of $f(t)=Ae^{-i\omega_0 t}$
149634
$ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$
144989
How i can find the fourier transform of $\frac{\sinh(ax)}{\sinh(\pi x)}$ where,$ |a| < \pi$
35754
Is $f(x)=\sin(x^2)$ periodic?
132448
Prove that: $\int_0^{n\pi}f(\cos^2(x))\,dx=n\int_0^{\pi}f(\cos^2(x))\,dx?$
95637
Justifying Calculations on $f(n)=\frac{1}{2 \pi}\int_{-\pi}^{\pi}\theta e^{-in \theta} d \theta$
124535
continuous function from $[\pi,2\pi]\to \mathbb{R}^2$