# Questions tagged [fourier-analysis]

Fourier analysis, also known as spectral analysis, encompasses all sorts of Fourier expansions, including Fourier series, Fourier transform and the discrete Fourier transform (and relatives). The non-commutative analog is (representation-theory).

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### Invariant continuous linear maps on group algebras

Let $G$ be a locally compact group and $M(G)=C^*_0(G)$. Assume that $\Gamma$ consists of all linear maps $T$ on $M(G)$ with $T\mu=\mu*\nu$ for some $\nu\in M(G)$. Q. Any characterization of $\Gamma$ ...
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### Basic doubt related to property of Fourier transform

Let $f\in L^1$ such that $\hat{f}\in L^1.$ $\hat{f}\in L^1\implies f$ is continuous. Define $g(x)=\begin{cases} 0 , \text{ if } x\in \mathbb{Q}\\ f(x), \text{ if } x\in \mathbb{Q}^c \end{cases} .$...
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### Why can't we measure a monochromatic wave's frequency perfectly over a finite range?

In Fourier analysis it is said that the only way to have 0 uncertainty in a monochromatic wave's frequency is if you FT it over an infinite domain (otherwise it does not produce a delta function). ...