Norm of a function

  • Thread starter Dragonfall
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  • #1
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Suppose [tex]\mathbb{T}=[-\pi,\pi][/tex] and we have a function in [tex]L^p(\mathbb{T})[/tex] with some measure. If we know the Fourier coefficients of f, what is the [tex]L^p[/tex] norm of f? Is it [tex](\sum f_i^p)^{1/p}[/tex]? where fi are the coefs.
 

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  • #2
AKG
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Is this a question about the definition of the Lp norm? For f, it would be:

[tex]\left (\int _{\mathbb{T}}|f|^p\, d\mu \right )^{\frac{1}{p}}[/tex]

where [itex]\mu[/itex] is the measure. Haven't looked at Fourier coefficients yet, so I can't answer your question, but I suspect what you put is wrong because it's missing absolute value signs.
 

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