Questions tagged [convolution]
Questions on the (continuous or discrete) convolution of two functions. It can also be used for questions about convolution of distributions (in the Schwartz's sense) or measures.
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Is there a name for non sparse linear operators which are products of convolution-like all-but-oneunities?
Is there a name for non sparse linear operators which are products of convolution-like all-but-one unities?
I suppose I will have to apologize for the cryptic question phrasing, but I really could not ...
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Finding the general convolution of probability function with hypergeometric PDFs.
I am trying to find the generalized convolution of this PDF distribution.
$$f(n, \sigma; v)= \frac{2^{\frac{3}{2}-\frac{n}{2}} \sigma ^{-n-1} v^\frac{n - 1}{2} K_{\frac{ n - 1}{2}}\left(\frac{v}{\...
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Integration of the product of a compact supported convolution [closed]
I know that in general case we have $$\int_{-\infty}^{+\infty}\int_{-\infty}^{+\infty} f(s)g(t-s) ds dt = \left( \int_{-\infty}^{+\infty} f(t) dt \right) \left( \int_{-\infty}^{+\infty}g(t) dt \right) ...
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Solving 1st order PDE including convolution
I'm studying Van Kampen's "Stochastic processes in physics and chemistry" and stuck to some exercise (p.78):
That is, solving
\begin{equation}
\frac{\partial P(y, t)}{\partial t}=\int_{-\...
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Is the Hadamard Product of two laplacian operators allowed to get some kind of biharmonic operator?
I'm currently working on my masters thesis in computer science and from this point I'm not that into this subject. Right know I try to understand the steps the authors of this paper did to get the ...
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Is there an exact expression for the full width half maximum of a sech^2 curve convolved on itself?
As some simple math can show, a Gaussian convolved onto itself is also a Gaussian. Importantly, the FWHM of the original gaussian compared to that of its convolved counterpart is different by a factor ...
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Matrix multiplication expressed as convolutions? [closed]
I know that the 2D discrete convolution operation can be expressed as a sparse matrix multiplication, but can the reverse be done easily? Does anyone know if there is a way to express any matrix ...
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Proving a distribution is not infinitely divisible
I'm trying to show the following:
Show that the distribution on $\mathbb R$ with density $f(x) = \frac{1-\cos(x)}{\pi x^2}$ is not infinitely divisible.
The characteristic function of this ...
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Evaluating the convolution of $e^{-at^2}$ and $e^{-bt^2}$ via Fourier transforms
Problem Statement: Use the convolution theorem on the function $ f(t) = e^{-at^2} $ and $ f(t) = e^{-bt^2} $, $ a, b \in \mathbb{R} $. Calculate $ (f \ast g)(t) $.
I got a hint that I should first ...
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Convolution between $L^1$ function and a singular integral kernel
I meet a problem when reading Modern Fourier Analysis(3rd. Edition) written by L.Grafakos. On pg.82 he writes:
Fix $L\in\mathbb{Z}^+$. Suppose that $\{K_j(x)\}_{j=1}^L$ is a family of functions ...
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How to prove $(F\ast\sin)(x)=-\sin(x)$, where $F(x)=\frac{1}{2}|x|$?
Wikipedia states in this article about fundamental solutions that if $F\left( x \right) = \tfrac{1}{2} \left| x \right|$, then
$$\left( F \ast \sin \right)\left( x \right) := \int\limits_{-\infty}^{\...
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convolution of the fundamental solution with the homogeneous solution
I have a question about the convolution of the fundamental solution with the homogeneous solution. Namely if the 2 are convoluble then the homogeneous solution is necessarily zero?
Let $U$ and $E$ ...
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Analycity of $f*g$ with $f$ and $g$ smooth on $\mathbb{R}$ and analytic on $\mathbb{R}^*$
Posted also on MO with a bounty
Suppose that we have two real functions $f$ and $g$ both belonging to $\mathcal{C}^\infty(\mathbb{R},\mathbb{R})$ analytic on $\mathbb{R}\backslash\{0\}$ but non-...
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Algorithm to compute a convolution recursively
Let
$$
f(t) = \int_0^t k(t-s)g(s) \, ds.
$$
Assume that $g$ is only given in a grid $t_j = j\delta_t$, and that we wish to compute similarly $f$ on the same grid.
What's an efficient algorithm to ...
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Clarification Needed on 1D Convolution and Kernel Purpose
I am confused about the definition of 1D convolution.
Given $ a = [-\frac{1}{2}, \frac{1}{2}] $ and $b = [1, 1, 1, -1, -1, -1] $, what will be the result of the convolution $( a * b )$?
From my ...
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