1
$\begingroup$

I've encountered two different notations for the delta distribution: $$\delta(x,y)$$ and $$\delta(x-y)$$ What is the difference between these two notations. Do they depend on context or should I prefer one over the other?

|cite|improve this question
$\endgroup$
  • 1
    $\begingroup$ The first one is not sufficiently standard for me to even know the intended meaning. The second one is quite standard (if the variable of integration is $x$, then this can be understood as a point mass of $1$ at $y$). $\endgroup$ – Ian Mar 29 '17 at 17:33
  • $\begingroup$ If the domain / space isn't additive, then $x-y$ makes no sense. But usually one writes $\delta_y$ if the mass is centered at $y$. $\endgroup$ – user251257 Mar 29 '17 at 17:38
2
$\begingroup$

The first describes a delta function acting at the origin.

point

The second describes a delta function acting along the line $x=y$:

line

|cite|improve this answer
$\endgroup$
0
$\begingroup$

The first notation is more convenient when working in high dimensions, since it naturally generalizes to $n$ dimensions: e.g., $\delta (x,y,z,w, ...)$. You can do this with the second notation $\delta(x) \delta(y), ...$

Certain software (e.g., Mathematica) supports both usages.

|cite|improve this answer
$\endgroup$
  • $\begingroup$ Thanks for your help with the Mathematica graphics. $\endgroup$ – dantopa Mar 29 '17 at 23:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.