Tagged Questions
4
votes
4answers
91 views
what is the relation of smooth compact supported funtions and real analytic function?
What is the major difference between real analytic and test function (smooth compact supported functions). Can we find a real analytic function $f$ on $R^n$ which is also smooth compact supported? If ...
1
vote
3answers
58 views
How can you show that $\delta′=f(0)\delta′−f′(0)\delta$ for a function f that is infinitely differentiable?
Assume that $f$ is infinitely differentiable. Let $\delta$ be the (Dirac) delta functional.
I know that $f\delta = f(0)\delta$, but I'm not sure how to derive the equation ...
1
vote
2answers
96 views
Dirac delta function
1)Prove that the dirac delta function property:
$$ x\delta'(x)=-\delta(x)$$
2)and :
$$\int_{-\infty}^\infty \delta'(x)f(x)dx=-f'(0) \ $$
3
votes
1answer
66 views
Prove the Borel Lemma
I'm trying to prove the Borel Lemma, which is:
For every series $a_0,a_1,a_2,\dots$ in $\mathbb{C}$ exists $f \in C^{\infty}(\mathbb{R})$ such as $$ f^{(k)}(0) = a_k $$ for every $k \in ...
2
votes
0answers
147 views
Does $\sqrt{\delta^2}$ make more sense than $\delta^2$?
What is the Product of $\delta$ functions with
itself? was already
asked some time ago. In a
comment
the OP states:
I want to create $\delta(t)$ such that the product with itself is also ...
3
votes
4answers
983 views
Which of these two ways to take the derivative of a delta function times another function is correct?
A well known identity of the Dirac delta function is that for any function $f(x)$:
$$
\delta(x) f(x) = \delta(x) f(0).
$$
If we take the derivative of the right hand side we get:
$$
...
