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 29, 2025 · Dirac’s delta function is considered (notation for) a distribution. Specifically it is (and its derivatives are) expressed in terms of the Radon-Nikodym derivative (s) of the …

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, 2023 · The Dirac delta is defined as a distribution by $$ \langle \delta_0,\varphi\rangle = \varphi (0). $$ The compact support is actually not needed for $\varphi$ because the value …

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 …

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.

Oct 11, 2020 · Sometimes considering the delta function is dimensionless is fine but the dimension needs to be fixed by its coefficient, namely the coefficient of the delta function …

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 …

Jul 16, 2013 · 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 …

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 …