# Questions tagged [fourier-transform]

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### Distribution boundary value of analytic function and wave front sets

Assume $f(z)$ is analytic in the tube domain $\mathbb R^n\oplus iC$, where $C\subset \mathbb R^n$ is a convex cone. Under the assumption $|f(x+iy)|\leq 1/|y|^k$, we know by a Theorem of Martineau (see ...
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### How to calculate Fourier transformation of eigenstates in CV quantum information [closed]

The position $\hat{q}$ and momentum $\hat{p}$ has $[\hat{q},\hat{p}]=i$. And we set there eigenstates as $|s\rangle_q$ and $|s\rangle_p$ with eigenvalue s. In the paper [Phy Rev A. 79, 062318 (2009)],...
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### How related are Fourier transforms on finite groups and Fourier transforms on graphs?

Here are two generalizations of the notion of a Fourier transform. I am also aware of the Pontryagin Duality generalization for locally compact abelian groups, though I am personally more concerned ...
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### Fourier transform on Minkowski space

Physicists Some people like to define the "Fourier transform" on Minkowski space as $\hat f(\xi) = \int e^{i \eta(x,\xi)} f(x) dx$, where $\eta(x,\xi)$ is the Minkowski form. I'm used to thinking of ...
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### Wavelet momentum identity

I am reading an article on wavelet connection coefficients (G. Beylkin, "On the representation of operators in bases of compactly supported wavelets", 1992 (MSN)) and I came across Equation (3.31): \...
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### Advantage of fractional Fourier transform over multiscale wavelet

What is the best argument of fractional Fourier transform over multiscale wavelet in data analysis purpose. Optimization of the good time-frequency domain parameter ? "Good" will be, find the %time-%...
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### Why is the Fourier transform so ubiquitous?

Many operations and equivalences in mathematics arise as some sort of Fourier transform. By Fourier transform I mean the following: Let $X$ and $Y$ be two objects of some category with products, and ...
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### Can Mellin transform be applied in this function? What's the result?

$$f(x) = \mathop {\lim }\limits_{T \to \infty } {i}\int_{-1/2-i\,T}^{-1/2+i\,T} \frac{(x-1)^{s}}{2^{s+1}}\,\frac{1}{sin(\pi*s)\,}\,\frac{ds}{s}$$
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### Translated version of a Caratheodory article

This excellent introduction to Compressive Sensing cites a couple of (seemingly) interesting Caratheodory papers from 1907-1911. These are:  C. Caratheodory. Uber den Variabilitätsbereich der ...