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If p(z)=a0+a1z+...+anz^n, and max|p(z)|=M for |z|=1, show that each coefficient ak is bounded by M.

I'm trying to take derivatives but it's not getting anywhere. Thanks!
 
If p(z)=a0+a1z+...+anz^n, and max|p(z)|=M for |z|=1, show that each coefficient ak is bounded by M.

I'm trying to take derivatives but it's not getting anywhere. Thanks!
Did you replace z with:

[tex]exp(i \theta)[/tex]

I suppose differentiating with respect to theata would make sence:

This would give you:

[tex]\sum_0^Na_n(-i)^n exp(-i n \theta)=\sum_0^Na_n exp(i n (\theta+\pi/2))=\sum_0^Na_n (i Z)^n[/tex]

Yeah, I'm stuck to.
 
Last edited:

mathwonk

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does cauchy's formula help?
 
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