# Tagged Questions

Use this tag for questions about Schwartz distributions, also known as Generalised Functions. For questions about "probability distributions", use (probability-distributions). For questions about distributions as sub-bundles of a vector bundle, use (differential-geometry).

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### How to prove that $x \rightarrow e^{1/x}$ is not a restriction of any real distribution to $\mathbb {R}_+$?

This is an excercise 2.2 from Hormander, vol. I: Does there exist a distribution $u$ on $\mathbb{R}$ with the restriction $x \rightarrow e^{1/x}$ to $\mathbb{R}_+$? The answer, provided in the book, ...
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### Hankel transform of a Bessel function of different order

Here I found that $$\int_0^\infty J_\nu(kr) J_\nu(sr) r dr = \frac{\delta(k - s)}{s} = \frac{1}{s^2}\delta\left(1 - \frac{k}{s}\right).$$ I wonder how can that be derived and if a similar method can ...
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### Derivative of a Delta function

I know questions similar to this one have been asked, but there is a particular aspect that I'm confused about that wasn't addressed in the answers to the other ones. I'm dealing with an expression ...
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### Reference for “distributional derivative being zero implies being constant”

I know that if a distribution (generalized function) has zero derivative, then it is a constant. I also know the proof. But I have a hard time finding a reference which contains a statement of this ...
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### Is this operator a Fourier multiplier operator?

I want to study the Fourier transform of $$L_{\alpha}(t) = \frac{e^{i\alpha t}}{t^2} - i\frac{\alpha}{t}$$ Basically i am trying to get a grip on, given a $f$, what is $f(t)\ast L_{\alpha}(t)$ and am ...
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### Do Electrical Engineering Researchers Usually Know Higher Math? e.g. Measure and Distribution Theory, Functional Analysis

I am an EE undergraduate student, and I recently took two courses in signals and systems. We were exposed to things like the Dirac delta (without mention of distributions), Fourier series (without ...
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### Fourier Transform of a Polynomial

Lets say you are given $$f(x)=1+x^3$$ and the definition of Fourier transform: \hat{f}(k)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}e^{-ikx}f(x)dx, ...
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### Why do we give $C_c^\infty(\mathbb{R}^d)$ the topology induced by all good seminorms?

Briefly, my question boils down to the following: What benefits do we gain from considering the space of test functions in the topology induced by all "good" seminorms, as opposed to other topologies ...
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### Why are chains topologically analoguous to distributions?

This question is related to my other question here but is different enough that I thought I might ask separately. At the nLab page on rational homotopy theory it is stated that chains are ...