New posts in Fourier Analysis

Show that $f_{k}\longrightarrow f$ both weakly in $L^{p}$ and a.e. implies $|f_{k}|^{p}-|f|^{p}-|f_{k}-f|^{p}$ converges to $0$ in distribution

For $p\geqslant 1$ there is some $f\in L^1$ s.t. $\sum_{k\in \Bbb Z }|\hat f(k)|^p=\infty $

Convolution of an $L^p$ function with a Compactly supported continuous function. What does it give?

For $\alpha>0$, evaluate $\int^{+\infty}_0xe^{-x}\cos x\cos(x^2/\alpha)\,dx$

Characteristic functions agree in a neighborhood of zero

Why are variance and expected value all we care about?

About Rudin's outline to proving that Lipschitz functions have converging Fourier Series

Existence of a certain Schwartz function with compact Fourier support

Show that $\int_{-\infty}^{\infty}f(x)\overline {g(x)}dx = \frac{1}{2\pi}\int_{-\infty}^{\infty} \hat{f}(\mu)\overline{\hat{g}(\mu)}d\mu.$

Proving $ \sum_{n \in \mathbb{Z} } \left[\frac{\sin (n \alpha + \theta) }{ n \alpha + \theta} \right]^2 = \frac{\pi}{\alpha} $