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Thread: Bessel's Inequality

  1. #1
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    Bessel's Inequality

    I'm trying to workout the proof for Bessel's Inequality as given in my text. I'm having trouble reconciling the version in my text with other sources. I attached screen shot of a version in my text, along with a version from another source. The one with A's and B's is from my text.

    Bessel's Inequality-bessel-both.png

    Should the inner product in the numerator be <B,Ai> ?
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  2. #2
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    Re: Bessel's Inequality

    yes.

    $B$ is the element in Hilbert space being described.

    The $A_i$'s are the orthonormal sequences
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