# Questions tagged [convolution]

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### Integral operator (compactness)

I am studying the compactness of some convolution operators. Let the convolution $$\Gamma: X\longrightarrow X; x\mapsto\int_0^t T(t-s)B(s)x\mathrm{d}s.$$ Here $T(\cdot)$ is a $C_0$-semigroup on some ...
• 309
1 vote
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+50

### Special function: Pulse peak modified with a power term

PeakFit (Systat, v. 4.12) is a software for fitting experimental peaks obtained in physics or chemical experiments. Under the miscellenous peak functions, it shows the following equations with a name, ...
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1 vote
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### Apply gaussian blur to get original image

Suppose I have an image A. Is it possible to construct an image A' from A so I can get the ...
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### Local Rankin-Selberg Zeta-function and Coates' p-adic L-Functions

$\DeclareMathOperator\Kern{Kern}\DeclareMathOperator\diag{diag}$ Let $F$ be a non-archimedean local field, $\mathcal{O}$ its ring of integers, $\mathfrak{p}$ its maximal ideal and $\pi$ a uniformizer. ...
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### Subtle distinction in "completeness"?

This is somewhat vague, but please bear with me. Complete metric spaces are supposed to take care of "gaps", they're understood as a natural extension of dense sets. The convolution, defined ...
134 views

• 1
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### 2-Wasserstein metric on convolution of probability distributions

I have two related questions. Let $\mu$ and $\nu$ be two distinct probability measures on $\mathbb{R}^n$ with finite second moments, and $W_2(\cdot,\cdot)$ be the $2$-Wasserstein metric. The question ...
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### Equivalent of a local limit theorem in the large deviation region and asymptotics of a convolution operator

Let $\{X_i \}_{i \in \mathbb{N}}$ be a sequence of i.i.d. random variables satisfying $\mathbb{E} X_1 = 0$ and $\mathbb{E} X_1 ^2 < \infty$. Assume that $\{S_n \}_{n \in \mathbb{N}}$ is a non-...
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### Recovering a function from its Gaussian convolution

Let $\varphi(x)=\frac{1}{\sqrt{2\pi}}\exp(-x^2/2)$ be the Gaussian density and $f:\mathbb{R}\to\mathbb{R}$ another measurable function. Under what conditions can $f$ be recovered from its convolution ...
155 views

### Vector convolution?

I am working on a research problem which leads to the following optimization problem: \begin{equation} \hat{M} = \operatorname*{arg\,max}_M \Bigl\lVert\sum_{k=0}^{M-1} {\mathbf y}_k \exp\left(-j 2\pi ...
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### Inverting convolutions over finite intervals

There are well-known techniques for inverting convolutions over the whole or half real line with Fourier and Laplace transformations, but on the face of it they can't be applied to an integral ...
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Given that the convolution definition as far as I am aware is: $(f*g)(t) = \int_{-\infty}^\infty f(\tau)g(t-\tau)d\tau$ Here I see that the functions f and ...