# Generalized Functions

• Dec 5th 2012, 11:20 PM
mbempeni
Generalized Functions

Thanks a lot.
• Dec 6th 2012, 08:02 PM
chiro
Re: Generalized Functions
Hey mbempeni.

What definition do you have of a generalized function?
• Dec 11th 2012, 12:12 PM
mbempeni
Re: Generalized Functions

I mean Dirac δ function
• Dec 11th 2012, 09:53 PM
chiro
Re: Generalized Functions
Can you use the limiting function of the normal distribution (as variance goes to zero) to prove this?
• Dec 12th 2012, 09:33 AM
mbempeni
Re: Generalized Functions
@chiro
Can you explain what you mean? Thanks for your interest!
• Dec 12th 2012, 12:52 PM
chiro
Re: Generalized Functions
I mean the limiting formulation like these:

Dirac delta function - Wikipedia, the free encyclopedia

However I think a better way would be to use Laplace transforms to do this: have you used these before?
• Dec 13th 2012, 06:39 AM
mbempeni
Re: Generalized Functions
No, I haven 't.

Could you help me to solve it?
• Dec 13th 2012, 08:09 PM
chiro
Re: Generalized Functions
In laplace transforms you have the shift theorem which is referenced on the wiki site:

Laplace transform - Wikipedia, the free encyclopedia

Consider transforming both to Laplace space (frequency domain) and use the time-scaling and shift theorem to show that they are both equal Laplace transform functions.

Once you show that they are equal, then it follows that the functions are also equal.