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seen Mar 27 at 17:23

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awarded  Nice Question
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awarded  Popular Question
Feb
1
comment Fourier Coefficients and Hölder Continuity
Thank you for the great diagram and explanation. Is there a reason that this problem becomes easy again for $C^{\infty}$ functions?
Feb
1
comment Fourier Coefficients and Hölder Continuity
Thanks! Is there a text or paper where I can find this result?
Feb
1
accepted Fourier Coefficients and Hölder Continuity
Jan
30
comment Fourier Coefficients and Hölder Continuity
I'm not sure I understand the notation $\phi_{\nu}(D_x)u$
Jan
30
comment Fourier Coefficients and Hölder Continuity
That is a nice sufficient condition. I own Stein and Shakarchi, as far as I am aware they never tackled such complicated questions, have I skimmed over some section?
Jan
30
comment Fourier Coefficients and Hölder Continuity
Yes I used Bernstein's theorem to construct my counterexample above. Do you know of any functions that both satisfy $f\in \mathcal{l}^1(\ZZ)$ and $|\hat{f}(n)|\leq C_f|n|^{-\alpha}$ for some $\alpha>1/2$ but $f$ is not Holder continuous of order $\alpha$.
Jan
30
asked Fourier Coefficients and Hölder Continuity
Jan
28
awarded  Scholar
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28
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Jan
28
comment When does continuity imply holomorphy?
Thanks, I'll check those out!
Jan
28
accepted When does continuity imply holomorphy?
Jan
28
awarded  Student
Jan
28
asked When does continuity imply holomorphy?