Fdtxjr

Should a narrator ever describe things based on a character's view instead of facts?

Should I warn a new PhD Student?

How would a solely written language work mechanically

How to get directions in deep space?

Unfrosted light bulb

Capacitor electron flow

Why does the Persian emissary display a string of crowned skulls?

How can a new country break out from a developed country without war?

Writing in a Christian voice

How to test the sharpness of a knife?

Showing mass murder in a kid's book

Reason why a kingside attack is not justified

Air travel with refrigerated insulin

Why is "la Gestapo" feminine?

Strange behavior in TikZ draw command

Did I make a mistake by ccing email to boss to others?

When is the exact date for EOL of Ubuntu 14.04 LTS?

Friend wants my recommendation but I don't want to give it to him

Is this saw blade faulty?

"Oh no!" in Latin

Sort with assumptions

Asserting that Atheism and Theism are both faith based positions

How do you say "Trust your struggle." in French?

A seasonal riddle

real valued functions that are invariant under convolution

Linear Fit IssueCharacteristic functions of group-invariant probability distributionsIntuitive and convincing argument that functions are vectorsconvolution integral involving modified Bessel functions of the first kindApproximating convolution of two functions with Oh notationFunctions with closed-form expectations under Gaussian PDFPeriodic functions wrapped into polygons: is this a transformation, a convolution or a projection? (or none of them)How does the value of the following integral change when we scale the shape by a factor $k$?Functions that are easy to antidifferentiate but whose inverses are hard to antidifferentiateTransforming a single Gaussian into a mixture of Gaussians

3

$begingroup$

Consider the function $f(x) = e^-x^2$, notice that $f$ convoluted with itself is of the form $acdot f(bx+c)$ for reals $a, b$ and $c$. Another way of saying this is that the shape of the function $f(x)$ does not change when convoluted with itself. It only gets stretch and shifted.

Here is another such function: $f(x) = frac11+x^2$

I am interested in a categorization of all such functions. Is such a categorization known? I am interested in any resources discussing this topic. Thanks

calculus probability-distributions convolution

share|cite|improve this question

edited Mar 13 at 19:19

mrtaurho

6,04051641

asked Mar 13 at 19:16

mathewmathew

437215

$endgroup$

add a comment | 

3

$begingroup$

Consider the function $f(x) = e^-x^2$, notice that $f$ convoluted with itself is of the form $acdot f(bx+c)$ for reals $a, b$ and $c$. Another way of saying this is that the shape of the function $f(x)$ does not change when convoluted with itself. It only gets stretch and shifted.

Here is another such function: $f(x) = frac11+x^2$

I am interested in a categorization of all such functions. Is such a categorization known? I am interested in any resources discussing this topic. Thanks

calculus probability-distributions convolution

share|cite|improve this question

edited Mar 13 at 19:19

mrtaurho

6,04051641

asked Mar 13 at 19:16

mathewmathew

437215

$endgroup$

add a comment | 

$begingroup$

Consider the function $f(x) = e^-x^2$, notice that $f$ convoluted with itself is of the form $acdot f(bx+c)$ for reals $a, b$ and $c$. Another way of saying this is that the shape of the function $f(x)$ does not change when convoluted with itself. It only gets stretch and shifted.

Here is another such function: $f(x) = frac11+x^2$

I am interested in a categorization of all such functions. Is such a categorization known? I am interested in any resources discussing this topic. Thanks

calculus probability-distributions convolution

share|cite|improve this question

edited Mar 13 at 19:19

mrtaurho

6,04051641

asked Mar 13 at 19:16

mathewmathew

437215

$endgroup$

share|cite|improve this question

edited Mar 13 at 19:19

mrtaurho

6,04051641

asked Mar 13 at 19:16

mathewmathew

437215

share|cite|improve this question

edited Mar 13 at 19:19

mrtaurho

6,04051641

asked Mar 13 at 19:16

mathewmathew

437215

edited Mar 13 at 19:19

mrtaurho

6,04051641

edited Mar 13 at 19:19

mrtaurho

6,04051641

asked Mar 13 at 19:16

mathewmathew

437215

asked Mar 13 at 19:16

mathewmathew

437215