Sep 12, 2024 · The delta "function" is the multiplicative identity of the convolution algebra. That is, $$\int f (\tau)\delta (t-\tau)d\tau=\int f (t-\tau)\delta (\tau)d\tau=f (t)$$ This is essentially the …

The part which I can not understand why the Delta "function" makes sense only when it acts on another function and that too only inside an integral and how is a "functional" or "distribution" …

Aug 25, 2019 · On Wikipedia, the definition of the dirac delta function is given as: Suppose I have a function where at two points, the function goes to infinity. Given that the distance between …

Note that the usual definition of integration doesn't apply to the dirac delta function in one dimension, because it requires that the function be real-valued (or complex-valued, as …

Physicists' $\delta$ function is a peak with very small width, small compared to other scales in the problem but not infinitely small. So what I do to such inconsistency of $\delta$ function is to fall …

Using this definition and the fact that the $\delta$-distribution is half of the second derivative of the absolute value function, one can give a rigorous proof of the formula in the query.

Feb 12, 2021 · The Dirac delta function, $\delta (t)$, used in continuous time integrals, is different from the Kronecker delta function, $\delta [n]$, used in discrete time summations. Their effect …

Mar 9, 2016 · @kibble The Dirac Delta is not a function and it therefore is nonsensical to write $\delta (t-a)=0$.

First a small remark : the dirac delta is not strictly speaking a function, it's called a distribution. It's often defined as being the distribution such that $\int f (x) \delta (x) dx = f (0)$. Using that …

Sep 4, 2020 · 6 It is known that the Dirac delta function scales as follows: $$\delta (kx)=\frac {1} {|k|}\delta (x)$$ I have studied the proof for it, considering Dirac delta function as a limit of the …