The integral-transforms tag has no wiki summary.

**1**

vote

**1**answer

630 views

### Writing an integral equation as a partial differential equation

Hello,
Can anyone help me see how one can get from the following integral
$$\lambda\int_{\beta=0}^{y}\int_{\alpha=x}^{Q-\beta}e^{-\mu(\alpha-x)}f(\alpha,\beta)d\alpha ...

**0**

votes

**1**answer

128 views

### Floquet tranform of the derivative of a function $f(r)$

The derivative of the Floquet transform equals the Floquet tranform of the derivative.
But can the Floquet tranform of the derivative of a function $f(r)$ can be expressed in terms of the Floquet ...

**1**

vote

**0**answers

141 views

### Integral Transform Wanted

Hello! Imagine I have a function
$f(r_1, r_2) = \int_{-\infty}^\infty g(|r_1 - r_3|) g(|r_1 - r_4|) g(|r_2 - r_3|) g(|r_2 - r_4|) g(|r_3 - r_4|) \; d r_3 d r_4$
Is there a way I could get rid of ...

**8**

votes

**2**answers

375 views

### The relationship between Crofton formula and Radon transform.

The famous Crofton formula says that the length of a curve can be calculated by integral of the `line crossing' over the space of all oriented lines. My question is, is there a way to treat this ...

**3**

votes

**2**answers

465 views

### Fonction spéciale

Est-ce qu'il y a une fonction spéciale sous la forme suivante:
$$\int e^{-st}e^{-(\alpha/(1+t))}t^{\beta-1}(1+t)^{-(\beta-1)-\gamma}dt$$
ou
$$\int ...

**15**

votes

**2**answers

953 views

### Complex structure on $L^2(\mathbb R)$ generalizing the Hilbert transform.

The Hilbert transform on the real Hilbert space $L^2(\mathbb R)$ is the singular integral operator
$$
\mathcal H(f)(x) := \frac{1}{\pi} \int_{-\infty}^\infty \frac{1}{x-y} f(y) dy.
$$
It satisfies ...

**2**

votes

**1**answer

387 views

### Integral kernel of form $e^{-<x,y>^2}$

Let $K(x,y): \mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R}$ given by $K(x,y) = e^{-< x,y>^2}$ where $<\cdot,\cdot>$ denote the canonical inner product. Define integral operator ...

**8**

votes

**3**answers

1k views

### When I can safely assume that a function is a Laplace transform of other function?

If I have a function and I want to represent it as being the Laplace transform of another, that is, I want to be sure that there is $\hat{f}(s)$ such that my function $f(x)$ can be written as:
$f(x) ...

**10**

votes

**3**answers

584 views

### MacWilliams Identity for Asymptotic Weight Spectrum of a Code

Introduction
Let $C$ be a code of block length $n$ having $A_i^C$ words of Hamming weight $i$, for $i\in [n]$, where $[n]:=\{0,\ldots,n\}$. Then, the sequence $\{ A_i^C \}_{i \in [n]} $ is called the ...

**0**

votes

**1**answer

2k views

### From an integral equation to a differential equation

Hello,
I am wondering whether it is possible to convert the following integral equation to a partial differential equation.
where $J_0(t,x)$ is some given nonnegative function and $\nu>0$ is ...

**0**

votes

**1**answer

182 views

### Completeness of an “infinite mixture of gaussians” representation

Is there a complete "infinite mixture of gaussians representation" for densities? What I mean is, is there, for any reasonably big class of densities $\phi(x)$ I can come up with a function $c(\mu, ...

**3**

votes

**0**answers

293 views

### inverse Laplace transform of $\delta_1(\cdot)$

Let's try to find a function $\psi(x)$ such that for Laplace transform $\tilde{f}(p)=\int_0^{\infty} f(y) e^{-py} dy$ one has $f(x)=\int_0^{\infty} \tilde{f}(p)\psi(px)dp$ (here we do not specify ...