Oct 4, 2015 · Yesterday a friend asked me what a Dirac delta function really is. I tried to explain it but eventually confused myself. It seems that a Dirac delta is defined as a function that …

Sep 12, 2024 · Explore related questions convolution dirac-delta See similar questions with these tags.

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 23, 2022 · Is Dirac delta a function? What is its contribution to analysis? What I know about it: It is infinite at 0 and 0 everywhere else. Its integration is 1 and I know how does it come.

45 I am given to understand that the Dirac delta function is strictly not a function in the conventional sense and it is a "functional or a distribution".

Sep 11, 2020 · The Dirac Delta is simply NOT a function (it is a Generalized Function). And use of an integral operator symbol to represent the functional $\langle \delta,\phi\rangle$ is abuse of …

Dec 27, 2021 · So, if we accept, that the above is the real meaning of \begin {equation*} \int_ {-\infty}^\infty \delta (x) f (x) dx =f (0) \end {equation*} then, we have proved the f (0) property, for …

Don't understand the integral over the square of the Dirac delta function Ask Question Asked 13 years ago Modified 1 year, 2 months ago

Feb 20, 2023 · This should hold by definition of Dirac delta: limit of some sequence of function with property that $ \int_ {-\infty}^\infty \delta (x)\cdot g (x)dx = g (0)$. Checking this definition …