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Math Help - Generalized Functions

  1. #1
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    Generalized Functions

    I would estimate your help.

    Thanks a lot.
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  2. #2
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    Re: Generalized Functions

    Hey mbempeni.

    What definition do you have of a generalized function?
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  3. #3
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    Re: Generalized Functions

    Thank you for your answer.

    I mean Dirac δ function
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  4. #4
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    Re: Generalized Functions

    Can you use the limiting function of the normal distribution (as variance goes to zero) to prove this?
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  5. #5
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    Re: Generalized Functions

    @chiro
    Can you explain what you mean? Thanks for your interest!
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  6. #6
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    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?
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  7. #7
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    Re: Generalized Functions

    No, I haven 't.

    Could you help me to solve it?
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  8. #8
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    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.
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