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    Fourier Transformation : Even Function

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    A function h(x) is positive or zero for all values of x. Assume h(x) is even. If the Fourier transformation of h(x) is H(u) show that...
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    Q:
    A function h (x) is positive or zero for all values of x. Assume h(x) is even .If the Fourier transformation of h(x) is H(u) show that,

    For all u,
    |H(u)| <= |H(0)|

    (Note <= mean less than equal to)
    Show that as

    Solution:

    Let's consider the Fourier transform of a function h(x):
    ( 1)
    where function h(x) must comply with the condition
    ( 2)
    (otherwise the integral (1) doesn't exist)
    In general, (u) is a ...

    Solution Summary

    The Fourier Transformation of an Even Function is investigated. The solution is detailed and well presented.

    $2.19