Please post an actual problem so that we can limit our discussion around that.How do I calculate the limit as h goes to infinity
of
h* delta(1/h) ??
If I apply that to a test function phi, I get h*phi(1/h), and now? How do I know the limit is 0? I know it tends to 0, but why?
How do I calculate the limit as h goes to infinity
of
h* delta(1/h) ??
If I apply that to a test function phi, I get h*phi(1/h), and now? How do I know the limit is 0? I know it tends to 0, but why?
Please post an actual problem so that we can limit our discussion around that.
I wondered if you might mean the Dirac delta; but "delta" is used in many different ways! Context is essential, especially as you get farther into advanced subjects. For that matter, "distribution" means a lot of different things. Putting "Dirac delta" into your title would have helped set the context.
There's still a lot more context you could share, for the benefit of those who might not have the same textbook; notation at this level is not universal. I'm going to have to take some time looking into this, in case no one else looking at your question is more current on it than I am.
Meanwhile, can you tell us more about what the solution said, and show the work you have done? Anything you can add will make it easier for others to help you.
the context of my question is the following
https://en.wikipedia.org/wiki/Distribution_(mathematics)
Yes, I knew that much from what you showed of the definition. I was hoping for a little more specific context of what you have learned about it, and any pieces of notation that might differ from what we can both read there. Did you have any specific theorems, or any similar examples?
Since you haven't shown your work as I asked (and as we always ask), let's start working through it. Can you tell me what δ(1/h) is? Then we can think about the question, \(\displaystyle \displaystyle\lim_{h\to \infty} h \delta\left(\frac{1}{h}\right)\).
yeah, it is phi(1/h)
where phi is a test function compactly supported, which means that above an interval (a,b) it becomes exactly zero.
so for example the limit as h goes to infinity of delta(h), since it is phi(h) would be 0.
but here I have phi(1/h) which shouldn't be 0, or maybe it can be, but then it is multiplied by h (so infinity),so I don't know how to proceed
How do I calculate the limit as h goes to infinity of h* delta(1/h) ??
If I apply that to a test function phi, I get h*phi(1/h), and now? How do I know the limit is 0? I know it tends to 0, but why?