0
votes
0answers
24 views

Abel and Radon Transform

I am learning Radon and Abel transforms. As far as I understood, basically both the transforms are projection of a 3D object onto a 2D plane. Then what is the difference between both transforms? Under ...
1
vote
0answers
38 views

Property of Laplace transforms

I was looking at this answer to the question asked and I am curious about the $$\int_0^\infty F(u)g(u) du = \int_0^\infty f(u)G(u) du $$ relationship being used. I referred to the link provided in ...
1
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0answers
41 views

The Fourier Stieltjes transform is uniformly continuous

Let $G$ be a locally compact Abelian group and $\hat{G}$ be its dual group, that is the group of all complex functions $\gamma:G\to\mathbb C$ such that ...
3
votes
0answers
35 views

fancy about some properties of kernel functions at infinity

Consider the two common types of kernel functions $\sum\limits_{t=a}^bf(t)K(x,t)$ and $\int_a^bf(t)K(x,t)~dt$ , prove whether the following properties are correct or not: $1.$ If $K(x,t)$ is bounded ...
3
votes
0answers
104 views

Properties of Eigenfunctions of a Kernel

I'm a newbie and may be this question is bit simple for you but pardon me if it's too simple and provide me some references. I've and Kernel function $K(x,y)$ ...
4
votes
0answers
496 views

Do kernel functions of integral transforms have any special properties?

From the Wikipedia page on integral transforms, it states that: ...an integral transform is any transform $T$ of the following form: $$ (Tf)(u)=\int^{t_2}_{t_1}K(t,u)f(t)dt $$ ...There are ...
4
votes
2answers
180 views

Why does it seem I can't apply the Radon transform to the Helmholtz equation?

Say we a function $u$ and a bounded region $\Omega \subset \mathbb{R}^2$, such that $(\Delta+\lambda)u = 0$ everywhere, and $u=0$ on the boundary. We extend it to the entire plane by defining $u=0$ ...
0
votes
1answer
116 views

When to use the Functional Determinant in Polar Coordinate Transformation

I am currently learning about polar coordinate transformation, especially for integrating over certain regions. Let's say we have to calculate $\int_{n}{xy \; dx dy}$ Then I think the correct ...
0
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1answer
836 views

Inverse of Laplace transform

There is a very simple expression for the inverse of Fourier transform. What is the easiest known expression for the inverse Laplace transform? Moreover, what is the easiest way to prove it?