Recent content by cabin5

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    Proving Fourier Bessel Series Expansion with Limiting Procedures

    Homework Statement By appropriate limiting procedures prove the following expansion \frac{1}{\left(\rho^2+z^2\right)^{1/2}}=\int^{\infty}_{0} e^{-k\left|z\right|}J_{0}(k\rho)dk Homework Equations The Attempt at a Solution I tried to implicate the fourier-bessel series but it...
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    Proof of an inner product space

    oh, ****! you're right , It was supposed to be max norm! I miswrote the definition.
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    Proof of an inner product space

    so l_{\infty}^{2} defines that norm which is basically the square of root total sum of square of each element of 2 vectors defined over R^2 field. Eventually , I think that you're example is correct, but besides I have no idea about whether functions defined in l_{\infty}^{2} is bounded or...
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    Proof of an inner product space

    Sorry for so late reply: The definition of l_{\infty}^{n} : On the linear space V_{n}(F) with the infinity norm defined by \left\|x\right\|_p=\left[\sum^{\infty}_{i=1}\left|\alpha^{i}\right|^p\right]^{1/p} where x=(\alpha^i) . The corresponding linear space to this norm is denoted...
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    Proof of an inner product space

    I have no clue whether one must use a bounded function or not in order to prove that.
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    Proving the Inner Product Identity for Complex Numbers

    Homework Statement Prove that \left\langle\alpha x,y\right\rangle-\alpha\left\langle x,y\right\rangle=0 for \alpha=i where \left\langle x,y\right\rangle=\frac{1}{4}\left\{\left\|x+y\right\|^{2}-\left\|x-y\right\|^{2}+i\left\|x+iy\right\|^{2}-i\left\|x-iy\right\|^{2}\right\}...
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    Proof of an inner product space

    Finally, It worked :) I thought any ordered pair would work as a counterexample. Thanks a lot!
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    Proof of an inner product space

    well, I tried the parallelogram law for x=(0,3) and y=(2,5) and it perfectly worked on both sides of the equation. Should I choose the complex field for that space? What's wrong with that?
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    Proof of an inner product space

    thanks for the post!
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    Proof of an inner product space

    Is it a mathematically correct method?
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    Proof of an inner product space

    Homework Statement Prove that the normed linear space l_{\infty}^{2} is not an inner product space. Homework Equations parallelogram law; \left\|x+y\right\|^2+\left\|x-y\right\|^2=2\left\|x\right\|^2+2\left\|y\right\|^2 The Attempt at a Solution Well, I tried to apply...
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    Normed linear space and inner product space

    thanks for the post!
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    Normed linear space and inner product space

    yes,ok, but how should I write down the associated norm of a space which I don't know. the only thing that I can write down is the parallelogram law itself which automatically yields the same thing in terms of inner product of its associated norm. I am a bit confused...
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    Normed linear space and inner product space

    ah, do you mean positive definiteness or parallelogram law?
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    Normed linear space and inner product space

    I know all the sufficient properties for an inner product space, but how can I find a suitable example for this particular problem?