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Results tagged with integral-transforms
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user 20460
For questions about integral transforms, inlcuding the Fourier transform, Laplace transform, Radon transform, Mellin transform, Hankel transform etc.
3
votes
1
answer
251
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Integral operator defined on $two$ distinct dense subspaces
I have decided to edit my post a bit heavily for clarity. I was trying to be fairly general but it's hard to see what I'm asking so I've decided to limit myself to a specific example which will hopefu …
- 370
3
votes
2
answers
1k
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Inverse Hankel Transform
I was reading through Akhiezer's book Lectures on Integral Transforms and in chapter nine, he states that the Hankel transform is unitary for $\nu > -1$, so that for a suitable function, $f$,
$f(y) = …
- 370
1
vote
Accepted
Motivating the Bessel translation operator
After some thought, I decided to see what happens in the Fourier case. Since $j_{\alpha}$ is an eigenfunction of $D_{\alpha}$, it stood to reason that we should look to the following PDE in the Fourie …
- 370
1
vote
2
answers
362
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Motivating the Bessel translation operator
In a paper I am reading on the Hankel transform (this paper to be exact), I've come across a somewhat peculiar definition for a generalized translation operator. The operator is designed with a convol …
- 370